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Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities
Authors:
Gheorghe Comanici,
Eric Bieber,
Mike Schaekermann,
Ice Pasupat,
Noveen Sachdeva,
Inderjit Dhillon,
Marcel Blistein,
Ori Ram,
Dan Zhang,
Evan Rosen,
Luke Marris,
Sam Petulla,
Colin Gaffney,
Asaf Aharoni,
Nathan Lintz,
Tiago Cardal Pais,
Henrik Jacobsson,
Idan Szpektor,
Nan-Jiang Jiang,
Krishna Haridasan,
Ahmed Omran,
Nikunj Saunshi,
Dara Bahri,
Gaurav Mishra,
Eric Chu
, et al. (3284 additional authors not shown)
Abstract:
In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal unde…
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In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.
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Submitted 22 July, 2025; v1 submitted 7 July, 2025;
originally announced July 2025.
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MedGemma Technical Report
Authors:
Andrew Sellergren,
Sahar Kazemzadeh,
Tiam Jaroensri,
Atilla Kiraly,
Madeleine Traverse,
Timo Kohlberger,
Shawn Xu,
Fayaz Jamil,
Cían Hughes,
Charles Lau,
Justin Chen,
Fereshteh Mahvar,
Liron Yatziv,
Tiffany Chen,
Bram Sterling,
Stefanie Anna Baby,
Susanna Maria Baby,
Jeremy Lai,
Samuel Schmidgall,
Lu Yang,
Kejia Chen,
Per Bjornsson,
Shashir Reddy,
Ryan Brush,
Kenneth Philbrick
, et al. (56 additional authors not shown)
Abstract:
Artificial intelligence (AI) has significant potential in healthcare applications, but its training and deployment faces challenges due to healthcare's diverse data, complex tasks, and the need to preserve privacy. Foundation models that perform well on medical tasks and require less task-specific tuning data are critical to accelerate the development of healthcare AI applications. We introduce Me…
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Artificial intelligence (AI) has significant potential in healthcare applications, but its training and deployment faces challenges due to healthcare's diverse data, complex tasks, and the need to preserve privacy. Foundation models that perform well on medical tasks and require less task-specific tuning data are critical to accelerate the development of healthcare AI applications. We introduce MedGemma, a collection of medical vision-language foundation models based on Gemma 3 4B and 27B. MedGemma demonstrates advanced medical understanding and reasoning on images and text, significantly exceeding the performance of similar-sized generative models and approaching the performance of task-specific models, while maintaining the general capabilities of the Gemma 3 base models. For out-of-distribution tasks, MedGemma achieves 2.6-10% improvement on medical multimodal question answering, 15.5-18.1% improvement on chest X-ray finding classification, and 10.8% improvement on agentic evaluations compared to the base models. Fine-tuning MedGemma further improves performance in subdomains, reducing errors in electronic health record information retrieval by 50% and reaching comparable performance to existing specialized state-of-the-art methods for pneumothorax classification and histopathology patch classification. We additionally introduce MedSigLIP, a medically-tuned vision encoder derived from SigLIP. MedSigLIP powers the visual understanding capabilities of MedGemma and as an encoder achieves comparable or better performance than specialized medical image encoders. Taken together, the MedGemma collection provides a strong foundation of medical image and text capabilities, with potential to significantly accelerate medical research and development of downstream applications. The MedGemma collection, including tutorials and model weights, can be found at https://goo.gle/medgemma.
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Submitted 12 July, 2025; v1 submitted 7 July, 2025;
originally announced July 2025.
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Weighted Mean Frequencies: a handcraft Fourier feature for 4D Flow MRI segmentation
Authors:
Simon Perrin,
Sébastien Levilly,
Huajun Sun,
Harold Mouchère,
Jean-Michel Serfaty
Abstract:
In recent decades, the use of 4D Flow MRI images has enabled the quantification of velocity fields within a volume of interest and along the cardiac cycle. However, the lack of resolution and the presence of noise in these biomarkers are significant issues. As indicated by recent studies, it appears that biomarkers such as wall shear stress are particularly impacted by the poor resolution of vesse…
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In recent decades, the use of 4D Flow MRI images has enabled the quantification of velocity fields within a volume of interest and along the cardiac cycle. However, the lack of resolution and the presence of noise in these biomarkers are significant issues. As indicated by recent studies, it appears that biomarkers such as wall shear stress are particularly impacted by the poor resolution of vessel segmentation. The Phase Contrast Magnetic Resonance Angiography (PC-MRA) is the state-of-the-art method to facilitate segmentation. The objective of this work is to introduce a new handcraft feature that provides a novel visualisation of 4D Flow MRI images, which is useful in the segmentation task. This feature, termed Weighted Mean Frequencies (WMF), is capable of revealing the region in three dimensions where a voxel has been passed by pulsatile flow. Indeed, this feature is representative of the hull of all pulsatile velocity voxels. The value of the feature under discussion is illustrated by two experiments. The experiments involved segmenting 4D Flow MRI images using optimal thresholding and deep learning methods. The results obtained demonstrate a substantial enhancement in terms of IoU and Dice, with a respective increase of 0.12 and 0.13 in comparison with the PC-MRA feature, as evidenced by the deep learning task. This feature has the potential to yield valuable insights that could inform future segmentation processes in other vascular regions, such as the heart or the brain.
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Submitted 25 June, 2025;
originally announced June 2025.
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Gemma 3 Technical Report
Authors:
Gemma Team,
Aishwarya Kamath,
Johan Ferret,
Shreya Pathak,
Nino Vieillard,
Ramona Merhej,
Sarah Perrin,
Tatiana Matejovicova,
Alexandre Ramé,
Morgane Rivière,
Louis Rouillard,
Thomas Mesnard,
Geoffrey Cideron,
Jean-bastien Grill,
Sabela Ramos,
Edouard Yvinec,
Michelle Casbon,
Etienne Pot,
Ivo Penchev,
Gaël Liu,
Francesco Visin,
Kathleen Kenealy,
Lucas Beyer,
Xiaohai Zhai,
Anton Tsitsulin
, et al. (191 additional authors not shown)
Abstract:
We introduce Gemma 3, a multimodal addition to the Gemma family of lightweight open models, ranging in scale from 1 to 27 billion parameters. This version introduces vision understanding abilities, a wider coverage of languages and longer context - at least 128K tokens. We also change the architecture of the model to reduce the KV-cache memory that tends to explode with long context. This is achie…
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We introduce Gemma 3, a multimodal addition to the Gemma family of lightweight open models, ranging in scale from 1 to 27 billion parameters. This version introduces vision understanding abilities, a wider coverage of languages and longer context - at least 128K tokens. We also change the architecture of the model to reduce the KV-cache memory that tends to explode with long context. This is achieved by increasing the ratio of local to global attention layers, and keeping the span on local attention short. The Gemma 3 models are trained with distillation and achieve superior performance to Gemma 2 for both pre-trained and instruction finetuned versions. In particular, our novel post-training recipe significantly improves the math, chat, instruction-following and multilingual abilities, making Gemma3-4B-IT competitive with Gemma2-27B-IT and Gemma3-27B-IT comparable to Gemini-1.5-Pro across benchmarks. We release all our models to the community.
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Submitted 25 March, 2025;
originally announced March 2025.
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On Teacher Hacking in Language Model Distillation
Authors:
Daniil Tiapkin,
Daniele Calandriello,
Johan Ferret,
Sarah Perrin,
Nino Vieillard,
Alexandre Ramé,
Mathieu Blondel
Abstract:
Post-training of language models (LMs) increasingly relies on the following two stages: (i) knowledge distillation, where the LM is trained to imitate a larger teacher LM, and (ii) reinforcement learning from human feedback (RLHF), where the LM is aligned by optimizing a reward model. In the second RLHF stage, a well-known challenge is reward hacking, where the LM over-optimizes the reward model.…
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Post-training of language models (LMs) increasingly relies on the following two stages: (i) knowledge distillation, where the LM is trained to imitate a larger teacher LM, and (ii) reinforcement learning from human feedback (RLHF), where the LM is aligned by optimizing a reward model. In the second RLHF stage, a well-known challenge is reward hacking, where the LM over-optimizes the reward model. Such phenomenon is in line with Goodhart's law and can lead to degraded performance on the true objective. In this paper, we investigate whether a similar phenomenon, that we call teacher hacking, can occur during knowledge distillation. This could arise because the teacher LM is itself an imperfect approximation of the true distribution. To study this, we propose a controlled experimental setup involving: (i) an oracle LM representing the ground-truth distribution, (ii) a teacher LM distilled from the oracle, and (iii) a student LM distilled from the teacher. Our experiments reveal the following insights. When using a fixed offline dataset for distillation, teacher hacking occurs; moreover, we can detect it by observing when the optimization process deviates from polynomial convergence laws. In contrast, employing online data generation techniques effectively mitigates teacher hacking. More precisely, we identify data diversity as the key factor in preventing hacking. Overall, our findings provide a deeper understanding of the benefits and limitations of distillation for building robust and efficient LMs.
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Submitted 4 February, 2025;
originally announced February 2025.
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Mastering Board Games by External and Internal Planning with Language Models
Authors:
John Schultz,
Jakub Adamek,
Matej Jusup,
Marc Lanctot,
Michael Kaisers,
Sarah Perrin,
Daniel Hennes,
Jeremy Shar,
Cannada Lewis,
Anian Ruoss,
Tom Zahavy,
Petar Veličković,
Laurel Prince,
Satinder Singh,
Eric Malmi,
Nenad Tomašev
Abstract:
Advancing planning and reasoning capabilities of Large Language Models (LLMs) is one of the key prerequisites towards unlocking their potential for performing reliably in complex and impactful domains. In this paper, we aim to demonstrate this across board games (Chess, Fischer Random / Chess960, Connect Four, and Hex), and we show that search-based planning can yield significant improvements in L…
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Advancing planning and reasoning capabilities of Large Language Models (LLMs) is one of the key prerequisites towards unlocking their potential for performing reliably in complex and impactful domains. In this paper, we aim to demonstrate this across board games (Chess, Fischer Random / Chess960, Connect Four, and Hex), and we show that search-based planning can yield significant improvements in LLM game-playing strength. We introduce, compare and contrast two major approaches: In external search, the model guides Monte Carlo Tree Search (MCTS) rollouts and evaluations without calls to an external game engine, and in internal search, the model is trained to generate in-context a linearized tree of search and a resulting final choice. Both build on a language model pre-trained on relevant domain knowledge, reliably capturing the transition and value functions in the respective environments, with minimal hallucinations. We evaluate our LLM search implementations against game-specific state-of-the-art engines, showcasing substantial improvements in strength over the base model, and reaching Grandmaster-level performance in chess while operating closer to the human search budget. Our proposed approach, combining search with domain knowledge, is not specific to board games, hinting at more general future applications.
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Submitted 22 May, 2025; v1 submitted 2 December, 2024;
originally announced December 2024.
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Diversity-Rewarded CFG Distillation
Authors:
Geoffrey Cideron,
Andrea Agostinelli,
Johan Ferret,
Sertan Girgin,
Romuald Elie,
Olivier Bachem,
Sarah Perrin,
Alexandre Ramé
Abstract:
Generative models are transforming creative domains such as music generation, with inference-time strategies like Classifier-Free Guidance (CFG) playing a crucial role. However, CFG doubles inference cost while limiting originality and diversity across generated contents. In this paper, we introduce diversity-rewarded CFG distillation, a novel finetuning procedure that distills the strengths of CF…
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Generative models are transforming creative domains such as music generation, with inference-time strategies like Classifier-Free Guidance (CFG) playing a crucial role. However, CFG doubles inference cost while limiting originality and diversity across generated contents. In this paper, we introduce diversity-rewarded CFG distillation, a novel finetuning procedure that distills the strengths of CFG while addressing its limitations. Our approach optimises two training objectives: (1) a distillation objective, encouraging the model alone (without CFG) to imitate the CFG-augmented predictions, and (2) an RL objective with a diversity reward, promoting the generation of diverse outputs for a given prompt. By finetuning, we learn model weights with the ability to generate high-quality and diverse outputs, without any inference overhead. This also unlocks the potential of weight-based model merging strategies: by interpolating between the weights of two models (the first focusing on quality, the second on diversity), we can control the quality-diversity trade-off at deployment time, and even further boost performance. We conduct extensive experiments on the MusicLM (Agostinelli et al., 2023) text-to-music generative model, where our approach surpasses CFG in terms of quality-diversity Pareto optimality. According to human evaluators, our finetuned-then-merged model generates samples with higher quality-diversity than the base model augmented with CFG. Explore our generations at https://google-research.github.io/seanet/musiclm/diverse_music/.
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Submitted 8 October, 2024;
originally announced October 2024.
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NeuroPapyri: A Deep Attention Embedding Network for Handwritten Papyri Retrieval
Authors:
Giuseppe De Gregorio,
Simon Perrin,
Rodrigo C. G. Pena,
Isabelle Marthot-Santaniello,
Harold Mouchère
Abstract:
The intersection of computer vision and machine learning has emerged as a promising avenue for advancing historical research, facilitating a more profound exploration of our past. However, the application of machine learning approaches in historical palaeography is often met with criticism due to their perceived ``black box'' nature. In response to this challenge, we introduce NeuroPapyri, an inno…
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The intersection of computer vision and machine learning has emerged as a promising avenue for advancing historical research, facilitating a more profound exploration of our past. However, the application of machine learning approaches in historical palaeography is often met with criticism due to their perceived ``black box'' nature. In response to this challenge, we introduce NeuroPapyri, an innovative deep learning-based model specifically designed for the analysis of images containing ancient Greek papyri. To address concerns related to transparency and interpretability, the model incorporates an attention mechanism. This attention mechanism not only enhances the model's performance but also provides a visual representation of the image regions that significantly contribute to the decision-making process. Specifically calibrated for processing images of papyrus documents with lines of handwritten text, the model utilizes individual attention maps to inform the presence or absence of specific characters in the input image. This paper presents the NeuroPapyri model, including its architecture and training methodology. Results from the evaluation demonstrate NeuroPapyri's efficacy in document retrieval, showcasing its potential to advance the analysis of historical manuscripts.
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Submitted 14 August, 2024;
originally announced August 2024.
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Gemma 2: Improving Open Language Models at a Practical Size
Authors:
Gemma Team,
Morgane Riviere,
Shreya Pathak,
Pier Giuseppe Sessa,
Cassidy Hardin,
Surya Bhupatiraju,
Léonard Hussenot,
Thomas Mesnard,
Bobak Shahriari,
Alexandre Ramé,
Johan Ferret,
Peter Liu,
Pouya Tafti,
Abe Friesen,
Michelle Casbon,
Sabela Ramos,
Ravin Kumar,
Charline Le Lan,
Sammy Jerome,
Anton Tsitsulin,
Nino Vieillard,
Piotr Stanczyk,
Sertan Girgin,
Nikola Momchev,
Matt Hoffman
, et al. (173 additional authors not shown)
Abstract:
In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We al…
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In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.
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Submitted 2 October, 2024; v1 submitted 31 July, 2024;
originally announced August 2024.
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BOND: Aligning LLMs with Best-of-N Distillation
Authors:
Pier Giuseppe Sessa,
Robert Dadashi,
Léonard Hussenot,
Johan Ferret,
Nino Vieillard,
Alexandre Ramé,
Bobak Shariari,
Sarah Perrin,
Abe Friesen,
Geoffrey Cideron,
Sertan Girgin,
Piotr Stanczyk,
Andrea Michi,
Danila Sinopalnikov,
Sabela Ramos,
Amélie Héliou,
Aliaksei Severyn,
Matt Hoffman,
Nikola Momchev,
Olivier Bachem
Abstract:
Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its sign…
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Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its significant computational overhead at inference time. Specifically, BOND is a distribution matching algorithm that forces the distribution of generations from the policy to get closer to the Best-of-N distribution. We use the Jeffreys divergence (a linear combination of forward and backward KL) to balance between mode-covering and mode-seeking behavior, and derive an iterative formulation that utilizes a moving anchor for efficiency. We demonstrate the effectiveness of our approach and several design choices through experiments on abstractive summarization and Gemma models. Aligning Gemma policies with BOND outperforms other RLHF algorithms by improving results on several benchmarks.
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Submitted 19 July, 2024;
originally announced July 2024.
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Approximating the Core via Iterative Coalition Sampling
Authors:
Ian Gemp,
Marc Lanctot,
Luke Marris,
Yiran Mao,
Edgar Duéñez-Guzmán,
Sarah Perrin,
Andras Gyorgy,
Romuald Elie,
Georgios Piliouras,
Michael Kaisers,
Daniel Hennes,
Kalesha Bullard,
Kate Larson,
Yoram Bachrach
Abstract:
The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, a…
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The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications.
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Submitted 6 February, 2024;
originally announced February 2024.
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Learning Correlated Equilibria in Mean-Field Games
Authors:
Paul Muller,
Romuald Elie,
Mark Rowland,
Mathieu Lauriere,
Julien Perolat,
Sarah Perrin,
Matthieu Geist,
Georgios Piliouras,
Olivier Pietquin,
Karl Tuyls
Abstract:
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game theoretic analysis becomes effectively infeasible beyond a low number of players. Recent approaches have gone around this limitation by instead considering Mean-…
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The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game theoretic analysis becomes effectively infeasible beyond a low number of players. Recent approaches have gone around this limitation by instead considering Mean-Field games, an approximation of anonymous $N$-player games, where the number of players is infinite and the population's state distribution, instead of every individual player's state, is the object of interest. The practical computability of Mean-Field Nash equilibria, the most studied Mean-Field equilibrium to date, however, typically depends on beneficial non-generic structural properties such as monotonicity or contraction properties, which are required for known algorithms to converge. In this work, we provide an alternative route for studying Mean-Field games, by developing the concepts of Mean-Field correlated and coarse-correlated equilibria. We show that they can be efficiently learnt in \emph{all games}, without requiring any additional assumption on the structure of the game, using three classical algorithms. Furthermore, we establish correspondences between our notions and those already present in the literature, derive optimality bounds for the Mean-Field - $N$-player transition, and empirically demonstrate the convergence of these algorithms on simple games.
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Submitted 22 August, 2022;
originally announced August 2022.
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Learning in Mean Field Games: A Survey
Authors:
Mathieu Laurière,
Sarah Perrin,
Julien Pérolat,
Sertan Girgin,
Paul Muller,
Romuald Élie,
Matthieu Geist,
Olivier Pietquin
Abstract:
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malhamé, Mean Field Games (MFGs) rely on a mean-field approximation to allow the number of players to grow to infinity. Traditional methods for solving these games generally rely…
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Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malhamé, Mean Field Games (MFGs) rely on a mean-field approximation to allow the number of players to grow to infinity. Traditional methods for solving these games generally rely on solving partial or stochastic differential equations with a full knowledge of the model. Recently, Reinforcement Learning (RL) has appeared promising to solve complex problems at scale. The combination of RL and MFGs is promising to solve games at a very large scale both in terms of population size and environment complexity. In this survey, we review the quickly growing recent literature on RL methods to learn equilibria and social optima in MFGs. We first identify the most common settings (static, stationary, and evolutive) of MFGs. We then present a general framework for classical iterative methods (based on best-response computation or policy evaluation) to solve MFGs in an exact way. Building on these algorithms and the connection with Markov Decision Processes, we explain how RL can be used to learn MFG solutions in a model-free way. Last, we present numerical illustrations on a benchmark problem, and conclude with some perspectives.
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Submitted 26 July, 2024; v1 submitted 25 May, 2022;
originally announced May 2022.
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Scalable Deep Reinforcement Learning Algorithms for Mean Field Games
Authors:
Mathieu Laurière,
Sarah Perrin,
Sertan Girgin,
Paul Muller,
Ayush Jain,
Theophile Cabannes,
Georgios Piliouras,
Julien Pérolat,
Romuald Élie,
Olivier Pietquin,
Matthieu Geist
Abstract:
Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free reinforcement learning (RL) methods. One limiting factor to further scale up using RL is that existing algorithms to solve MFGs require the mixing of approximated quant…
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Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free reinforcement learning (RL) methods. One limiting factor to further scale up using RL is that existing algorithms to solve MFGs require the mixing of approximated quantities such as strategies or $q$-values. This is far from being trivial in the case of non-linear function approximation that enjoy good generalization properties, e.g. neural networks. We propose two methods to address this shortcoming. The first one learns a mixed strategy from distillation of historical data into a neural network and is applied to the Fictitious Play algorithm. The second one is an online mixing method based on regularization that does not require memorizing historical data or previous estimates. It is used to extend Online Mirror Descent. We demonstrate numerically that these methods efficiently enable the use of Deep RL algorithms to solve various MFGs. In addition, we show that these methods outperform SotA baselines from the literature.
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Submitted 17 June, 2022; v1 submitted 22 March, 2022;
originally announced March 2022.
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Solving N-player dynamic routing games with congestion: a mean field approach
Authors:
Theophile Cabannes,
Mathieu Lauriere,
Julien Perolat,
Raphael Marinier,
Sertan Girgin,
Sarah Perrin,
Olivier Pietquin,
Alexandre M. Bayen,
Eric Goubault,
Romuald Elie
Abstract:
The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can rep…
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The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps), this approach enables learning traffic dynamics with more than 14,000 vehicles.
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Submitted 27 October, 2021; v1 submitted 22 October, 2021;
originally announced October 2021.
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Generalization in Mean Field Games by Learning Master Policies
Authors:
Sarah Perrin,
Mathieu Laurière,
Julien Pérolat,
Romuald Élie,
Matthieu Geist,
Olivier Pietquin
Abstract:
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs. Machine Learning has the potential to solve a wider diversity of MFG problems thanks to generalizations capacities. We study how to leverage these generalization…
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Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs. Machine Learning has the potential to solve a wider diversity of MFG problems thanks to generalizations capacities. We study how to leverage these generalization properties to learn policies enabling a typical agent to behave optimally against any population distribution. In reference to the Master equation in MFGs, we coin the term ``Master policies'' to describe them and we prove that a single Master policy provides a Nash equilibrium, whatever the initial distribution. We propose a method to learn such Master policies. Our approach relies on three ingredients: adding the current population distribution as part of the observation, approximating Master policies with neural networks, and training via Reinforcement Learning and Fictitious Play. We illustrate on numerical examples not only the efficiency of the learned Master policy but also its generalization capabilities beyond the distributions used for training.
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Submitted 20 September, 2021;
originally announced September 2021.
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Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint
Authors:
Matthieu Geist,
Julien Pérolat,
Mathieu Laurière,
Romuald Elie,
Sarah Perrin,
Olivier Bachem,
Rémi Munos,
Olivier Pietquin
Abstract:
Concave Utility Reinforcement Learning (CURL) extends RL from linear to concave utilities in the occupancy measure induced by the agent's policy. This encompasses not only RL but also imitation learning and exploration, among others. Yet, this more general paradigm invalidates the classical Bellman equations, and calls for new algorithms. Mean-field Games (MFGs) are a continuous approximation of m…
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Concave Utility Reinforcement Learning (CURL) extends RL from linear to concave utilities in the occupancy measure induced by the agent's policy. This encompasses not only RL but also imitation learning and exploration, among others. Yet, this more general paradigm invalidates the classical Bellman equations, and calls for new algorithms. Mean-field Games (MFGs) are a continuous approximation of many-agent RL. They consider the limit case of a continuous distribution of identical agents, anonymous with symmetric interests, and reduce the problem to the study of a single representative agent in interaction with the full population. Our core contribution consists in showing that CURL is a subclass of MFGs. We think this important to bridge together both communities. It also allows to shed light on aspects of both fields: we show the equivalence between concavity in CURL and monotonicity in the associated MFG, between optimality conditions in CURL and Nash equilibrium in MFG, or that Fictitious Play (FP) for this class of MFGs is simply Frank-Wolfe, bringing the first convergence rate for discrete-time FP for MFGs. We also experimentally demonstrate that, using algorithms recently introduced for solving MFGs, we can address the CURL problem more efficiently.
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Submitted 16 February, 2022; v1 submitted 7 June, 2021;
originally announced June 2021.
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Mean Field Games Flock! The Reinforcement Learning Way
Authors:
Sarah Perrin,
Mathieu Laurière,
Julien Pérolat,
Matthieu Geist,
Romuald Élie,
Olivier Pietquin
Abstract:
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG), where each individual chooses its acceleration depending on the population be…
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We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG), where each individual chooses its acceleration depending on the population behavior. Combining Deep Reinforcement Learning (RL) and Normalizing Flows (NF), we obtain a tractable solution requiring only very weak assumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their velocity to match the neighboring flock's average one. We use Fictitious Play and alternate: (1) computing an approximate best response with Deep RL, and (2) estimating the next population distribution with NF. We show numerically that our algorithm learn multi-group or high-dimensional flocking with obstacles.
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Submitted 17 May, 2021;
originally announced May 2021.
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Scaling up Mean Field Games with Online Mirror Descent
Authors:
Julien Perolat,
Sarah Perrin,
Romuald Elie,
Mathieu Laurière,
Georgios Piliouras,
Matthieu Geist,
Karl Tuyls,
Olivier Pietquin
Abstract:
We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity assumptions. This theoretical result nicely extends to multi-population games and to settings involving common noise. A thorough experimental investigation on vari…
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We address scaling up equilibrium computation in Mean Field Games (MFGs) using Online Mirror Descent (OMD). We show that continuous-time OMD provably converges to a Nash equilibrium under a natural and well-motivated set of monotonicity assumptions. This theoretical result nicely extends to multi-population games and to settings involving common noise. A thorough experimental investigation on various single and multi-population MFGs shows that OMD outperforms traditional algorithms such as Fictitious Play (FP). We empirically show that OMD scales up and converges significantly faster than FP by solving, for the first time to our knowledge, examples of MFGs with hundreds of billions states. This study establishes the state-of-the-art for learning in large-scale multi-agent and multi-population games.
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Submitted 28 February, 2021;
originally announced March 2021.
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Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications
Authors:
Sarah Perrin,
Julien Perolat,
Mathieu Laurière,
Matthieu Geist,
Romuald Elie,
Olivier Pietquin
Abstract:
In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $γ$-discounted), allowing in particular for the introduction of an additional common noise.
We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced e…
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In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $γ$-discounted), allowing in particular for the introduction of an additional common noise.
We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate $O(\frac{1}{t})$. Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.
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Submitted 26 October, 2020; v1 submitted 5 July, 2020;
originally announced July 2020.
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Decision method choice in a human posture recognition context
Authors:
Stéphane Perrin,
Eric Benoit,
Didier Coquin
Abstract:
Human posture recognition provides a dynamic field that has produced many methods. Using fuzzy subsets based data fusion methods to aggregate the results given by different types of recognition processes is a convenient way to improve recognition methods. Nevertheless, choosing a defuzzification method to imple-ment the decision is a crucial point of this approach. The goal of this paper is to pre…
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Human posture recognition provides a dynamic field that has produced many methods. Using fuzzy subsets based data fusion methods to aggregate the results given by different types of recognition processes is a convenient way to improve recognition methods. Nevertheless, choosing a defuzzification method to imple-ment the decision is a crucial point of this approach. The goal of this paper is to present an approach where the choice of the defuzzification method is driven by the constraints of the final data user, which are expressed as limitations on indica-tors like confidence or accuracy. A practical experimentation illustrating this ap-proach is presented: from a depth camera sensor, human posture is interpreted and the defuzzification method is selected in accordance with the constraints of the final information consumer. The paper illustrates the interest of the approach in a context of postures based human robot communication.
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Submitted 11 July, 2018;
originally announced July 2018.