Bilal Piot

Gemma Team, Morgane Riviere, Shreya Pathak et al. · deepmind

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.

Julien Perolat, Bart de Vylder, Daniel Hennes et al.

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.

Mohammad Gheshlaghi Azar, Mark Rowland, Bilal Piot et al.

The prevalent deployment of learning from human preferences through reinforcement learning (RLHF) relies on two important approximations: the first assumes that pairwise preferences can be substituted with pointwise rewards. The second assumes that a reward model trained on these pointwise rewards can generalize from collected data to out-of-distribution data sampled by the policy. Recently, Direct Preference Optimisation (DPO) has been proposed as an approach that bypasses the second approximation and learn directly a policy from collected data without the reward modelling stage. However, this method still heavily relies on the first approximation. In this paper we try to gain a deeper theoretical understanding of these practical algorithms. In particular we derive a new general objective called $Ψ$PO for learning from human preferences that is expressed in terms of pairwise preferences and therefore bypasses both approximations. This new general objective allows us to perform an in-depth analysis of the behavior of RLHF and DPO (as special cases of $Ψ$PO) and to identify their potential pitfalls. We then consider another special case for $Ψ$PO by setting $Ψ$ simply to Identity, for which we can derive an efficient optimisation procedure, prove performance guarantees and demonstrate its empirical superiority to DPO on some illustrative examples.

Zhaohan Daniel Guo, Shantanu Thakoor, Miruna Pîslar et al.

We present BYOL-Explore, a conceptually simple yet general approach for curiosity-driven exploration in visually-complex environments. BYOL-Explore learns a world representation, the world dynamics, and an exploration policy all-together by optimizing a single prediction loss in the latent space with no additional auxiliary objective. We show that BYOL-Explore is effective in DM-HARD-8, a challenging partially-observable continuous-action hard-exploration benchmark with visually-rich 3-D environments. On this benchmark, we solve the majority of the tasks purely through augmenting the extrinsic reward with BYOL-Explore s intrinsic reward, whereas prior work could only get off the ground with human demonstrations. As further evidence of the generality of BYOL-Explore, we show that it achieves superhuman performance on the ten hardest exploration games in Atari while having a much simpler design than other competitive agents.

Yunhao Tang, Zhaohan Daniel Guo, Pierre Harvey Richemond et al.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Wei Xiong, Chengshuai Shi, Jiaming Shen et al.

Recent studies have shown that large language models' (LLMs) mathematical problem-solving capabilities can be enhanced by integrating external tools, such as code interpreters, and employing multi-turn Chain-of-Thought (CoT) reasoning. While current methods focus on synthetic data generation and Supervised Fine-Tuning (SFT), this paper studies the complementary direct preference learning approach to further improve model performance. However, existing direct preference learning algorithms are originally designed for the single-turn chat task, and do not fully address the complexities of multi-turn reasoning and external tool integration required for tool-integrated mathematical reasoning tasks. To fill in this gap, we introduce a multi-turn direct preference learning framework, tailored for this context, that leverages feedback from code interpreters and optimizes trajectory-level preferences. This framework includes multi-turn DPO and multi-turn KTO as specific implementations. The effectiveness of our framework is validated through training of various language models using an augmented prompt set from the GSM8K and MATH datasets. Our results demonstrate substantial improvements: a supervised fine-tuned Gemma-1.1-it-7B model's performance increased from 77.5% to 83.9% on GSM8K and from 46.1% to 51.2% on MATH. Similarly, a Gemma-2-it-9B model improved from 84.1% to 86.3% on GSM8K and from 51.0% to 54.5% on MATH.

Pierre H. Richemond, Allison Tam, Yunhao Tang et al.

Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new \emph{closed-form predictor} variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at $100$ and $300$ epochs (top-$1$ linear accuracy on ImageNet).

Yunhao Tang, Zhaohan Daniel Guo, Zeyu Zheng et al.

Offline preference optimization allows fine-tuning large models directly from offline data, and has proved effective in recent alignment practices. We propose generalized preference optimization (GPO), a family of offline losses parameterized by a general class of convex functions. GPO enables a unified view over preference optimization, encompassing existing algorithms such as DPO, IPO and SLiC as special cases, while naturally introducing new variants. The GPO framework also sheds light on how offline algorithms enforce regularization, through the design of the convex function that defines the loss. Our analysis and experiments reveal the connections and subtle differences between the offline regularization and the KL divergence regularization intended by the canonical RLHF formulation. In a controlled setting akin to Gao et al 2023, we also show that different GPO variants achieve similar trade-offs between regularization and performance, though the optimal values of hyper-parameter might differ as predicted by theory. In all, our results present new algorithmic toolkits and empirical insights to alignment practitioners.

Daniele Calandriello, Daniel Guo, Remi Munos et al.

Ensuring alignment of language models' outputs with human preferences is critical to guarantee a useful, safe, and pleasant user experience. Thus, human alignment has been extensively studied recently and several methods such as Reinforcement Learning from Human Feedback (RLHF), Direct Policy Optimisation (DPO) and Sequence Likelihood Calibration (SLiC) have emerged. In this paper, our contribution is two-fold. First, we show the equivalence between two recent alignment methods, namely Identity Policy Optimisation (IPO) and Nash Mirror Descent (Nash-MD). Second, we introduce a generalisation of IPO, named IPO-MD, that leverages the regularised sampling approach proposed by Nash-MD. This equivalence may seem surprising at first sight, since IPO is an offline method whereas Nash-MD is an online method using a preference model. However, this equivalence can be proven when we consider the online version of IPO, that is when both generations are sampled by the online policy and annotated by a trained preference model. Optimising the IPO loss with such a stream of data becomes then equivalent to finding the Nash equilibrium of the preference model through self-play. Building on this equivalence, we introduce the IPO-MD algorithm that generates data with a mixture policy (between the online and reference policy) similarly as the general Nash-MD algorithm. We compare online-IPO and IPO-MD to different online versions of existing losses on preference data such as DPO and SLiC on a summarisation task.

Lior Shani, Aviv Rosenberg, Asaf Cassel et al.

Reinforcement Learning from Human Feedback (RLHF) has become the standard approach for aligning Large Language Models (LLMs) with human preferences, allowing LLMs to demonstrate remarkable abilities in various tasks. Existing methods work by emulating the preferences at the single decision (turn) level, limiting their capabilities in settings that require planning or multi-turn interactions to achieve a long-term goal. In this paper, we address this issue by developing novel methods for Reinforcement Learning (RL) from preference feedback between two full multi-turn conversations. In the tabular setting, we present a novel mirror-descent-based policy optimization algorithm for the general multi-turn preference-based RL problem, and prove its convergence to Nash equilibrium. To evaluate performance, we create a new environment, Education Dialogue, where a teacher agent guides a student in learning a random topic, and show that a deep RL variant of our algorithm outperforms RLHF baselines. Finally, we show that in an environment with explicit rewards, our algorithm recovers the same performance as a reward-based RL baseline, despite relying solely on a weaker preference signal.

Alaa Saade, Steven Kapturowski, Daniele Calandriello et al.

We introduce Robust Exploration via Clustering-based Online Density Estimation (RECODE), a non-parametric method for novelty-based exploration that estimates visitation counts for clusters of states based on their similarity in a chosen embedding space. By adapting classical clustering to the nonstationary setting of Deep RL, RECODE can efficiently track state visitation counts over thousands of episodes. We further propose a novel generalization of the inverse dynamics loss, which leverages masked transformer architectures for multi-step prediction; which in conjunction with RECODE achieves a new state-of-the-art in a suite of challenging 3D-exploration tasks in DM-Hard-8. RECODE also sets new state-of-the-art in hard exploration Atari games, and is the first agent to reach the end screen in "Pitfall!".

Pedro A. Ortega, Markus Kunesch, Grégoire Delétang et al.

The recent phenomenal success of language models has reinvigorated machine learning research, and large sequence models such as transformers are being applied to a variety of domains. One important problem class that has remained relatively elusive however is purposeful adaptive behavior. Currently there is a common perception that sequence models "lack the understanding of the cause and effect of their actions" leading them to draw incorrect inferences due to auto-suggestive delusions. In this report we explain where this mismatch originates, and show that it can be resolved by treating actions as causal interventions. Finally, we show that in supervised learning, one can teach a system to condition or intervene on data by training with factual and counterfactual error signals respectively.

Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, Alaa Saade et al.

Exploration is essential for solving complex Reinforcement Learning (RL) tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration problem as a well-defined policy optimization problem whose solution aims at visiting all states as uniformly as possible. This is in contrast to standard uncertainty-based approaches where exploration is transient and eventually vanishes. However, existing approaches to MSVE are theoretically justified only for discrete state-spaces as they are oblivious to the geometry of continuous domains. We address this challenge by introducing Geometric Entropy Maximisation (GEM), a new algorithm that maximises the geometry-aware Shannon entropy of state-visits in both discrete and continuous domains. Our key theoretical contribution is casting geometry-aware MSVE exploration as a tractable problem of optimising a simple and novel noise-contrastive objective function. In our experiments, we show the efficiency of GEM in solving several RL problems with sparse rewards, compared against other deep RL exploration approaches.

Pierre H. Richemond, Jean-Bastien Grill, Florent Altché et al.

Bootstrap Your Own Latent (BYOL) is a self-supervised learning approach for image representation. From an augmented view of an image, BYOL trains an online network to predict a target network representation of a different augmented view of the same image. Unlike contrastive methods, BYOL does not explicitly use a repulsion term built from negative pairs in its training objective. Yet, it avoids collapse to a trivial, constant representation. Thus, it has recently been hypothesized that batch normalization (BN) is critical to prevent collapse in BYOL. Indeed, BN flows gradients across batch elements, and could leak information about negative views in the batch, which could act as an implicit negative (contrastive) term. However, we experimentally show that replacing BN with a batch-independent normalization scheme (namely, a combination of group normalization and weight standardization) achieves performance comparable to vanilla BYOL ($73.9\%$ vs. $74.3\%$ top-1 accuracy under the linear evaluation protocol on ImageNet with ResNet-$50$). Our finding disproves the hypothesis that the use of batch statistics is a crucial ingredient for BYOL to learn useful representations.

Jean-Bastien Grill, Florian Strub, Florent Altché et al.

We introduce Bootstrap Your Own Latent (BYOL), a new approach to self-supervised image representation learning. BYOL relies on two neural networks, referred to as online and target networks, that interact and learn from each other. From an augmented view of an image, we train the online network to predict the target network representation of the same image under a different augmented view. At the same time, we update the target network with a slow-moving average of the online network. While state-of-the art methods rely on negative pairs, BYOL achieves a new state of the art without them. BYOL reaches $74.3\%$ top-1 classification accuracy on ImageNet using a linear evaluation with a ResNet-50 architecture and $79.6\%$ with a larger ResNet. We show that BYOL performs on par or better than the current state of the art on both transfer and semi-supervised benchmarks. Our implementation and pretrained models are given on GitHub.

Daniel Guo, Bernardo Avila Pires, Bilal Piot et al.

Learning a good representation is an essential component for deep reinforcement learning (RL). Representation learning is especially important in multitask and partially observable settings where building a representation of the unknown environment is crucial to solve the tasks. Here we introduce Prediction of Bootstrap Latents (PBL), a simple and flexible self-supervised representation learning algorithm for multitask deep RL. PBL builds on multistep predictive representations of future observations, and focuses on capturing structured information about environment dynamics. Specifically, PBL trains its representation by predicting latent embeddings of future observations. These latent embeddings are themselves trained to be predictive of the aforementioned representations. These predictions form a bootstrapping effect, allowing the agent to learn more about the key aspects of the environment dynamics. In addition, by defining prediction tasks completely in latent space, PBL provides the flexibility of using multimodal observations involving pixel images, language instructions, rewards and more. We show in our experiments that PBL delivers across-the-board improved performance over state of the art deep RL agents in the DMLab-30 and Atari-57 multitask setting.

Adrià Puigdomènech Badia, Bilal Piot, Steven Kapturowski et al.

Atari games have been a long-standing benchmark in the reinforcement learning (RL) community for the past decade. This benchmark was proposed to test general competency of RL algorithms. Previous work has achieved good average performance by doing outstandingly well on many games of the set, but very poorly in several of the most challenging games. We propose Agent57, the first deep RL agent that outperforms the standard human benchmark on all 57 Atari games. To achieve this result, we train a neural network which parameterizes a family of policies ranging from very exploratory to purely exploitative. We propose an adaptive mechanism to choose which policy to prioritize throughout the training process. Additionally, we utilize a novel parameterization of the architecture that allows for more consistent and stable learning.

Anna Harutyunyan, Will Dabney, Thomas Mesnard et al.

We consider the problem of efficient credit assignment in reinforcement learning. In order to efficiently and meaningfully utilize new data, we propose to explicitly assign credit to past decisions based on the likelihood of them having led to the observed outcome. This approach uses new information in hindsight, rather than employing foresight. Somewhat surprisingly, we show that value functions can be rewritten through this lens, yielding a new family of algorithms. We study the properties of these algorithms, and empirically show that they successfully address important credit assignment challenges, through a set of illustrative tasks.

Mohammad Gheshlaghi Azar, Bilal Piot, Bernardo Avila Pires et al.

As humans we are driven by a strong desire for seeking novelty in our world. Also upon observing a novel pattern we are capable of refining our understanding of the world based on the new information---humans can discover their world. The outstanding ability of the human mind for discovery has led to many breakthroughs in science, art and technology. Here we investigate the possibility of building an agent capable of discovering its world using the modern AI technology. In particular we introduce NDIGO, Neural Differential Information Gain Optimisation, a self-supervised discovery model that aims at seeking new information to construct a global view of its world from partial and noisy observations. Our experiments on some controlled 2-D navigation tasks show that NDIGO outperforms state-of-the-art information-seeking methods in terms of the quality of the learned representation. The improvement in performance is particularly significant in the presence of white or structured noise where other information-seeking methods follow the noise instead of discovering their world.

Zhaohan Daniel Guo, Mohammad Gheshlaghi Azar, Bilal Piot et al.

Unsupervised representation learning has succeeded with excellent results in many applications. It is an especially powerful tool to learn a good representation of environments with partial or noisy observations. In partially observable domains it is important for the representation to encode a belief state, a sufficient statistic of the observations seen so far. In this paper, we investigate whether it is possible to learn such a belief representation using modern neural architectures. Specifically, we focus on one-step frame prediction and two variants of contrastive predictive coding (CPC) as the objective functions to learn the representations. To evaluate these learned representations, we test how well they can predict various pieces of information about the underlying state of the environment, e.g., position of the agent in a 3D maze. We show that all three methods are able to learn belief representations of the environment, they encode not only the state information, but also its uncertainty, a crucial aspect of belief states. We also find that for CPC multi-step predictions and action-conditioning are critical for accurate belief representations in visually complex environments. The ability of neural representations to capture the belief information has the potential to spur new advances for learning and planning in partially observable domains, where leveraging uncertainty is essential for optimal decision making.

Julien Perolat, Mateusz Malinowski, Bilal Piot et al.

We study the problem of learning classifiers robust to universal adversarial perturbations. While prior work approaches this problem via robust optimization, adversarial training, or input transformation, we instead phrase it as a two-player zero-sum game. In this new formulation, both players simultaneously play the same game, where one player chooses a classifier that minimizes a classification loss whilst the other player creates an adversarial perturbation that increases the same loss when applied to every sample in the training set. By observing that performing a classification (respectively creating adversarial samples) is the best response to the other player, we propose a novel extension of a game-theoretic algorithm, namely fictitious play, to the domain of training robust classifiers. Finally, we empirically show the robustness and versatility of our approach in two defence scenarios where universal attacks are performed on several image classification datasets -- CIFAR10, CIFAR100 and ImageNet.

Tobias Pohlen, Bilal Piot, Todd Hester et al.

Despite significant advances in the field of deep Reinforcement Learning (RL), today's algorithms still fail to learn human-level policies consistently over a set of diverse tasks such as Atari 2600 games. We identify three key challenges that any algorithm needs to master in order to perform well on all games: processing diverse reward distributions, reasoning over long time horizons, and exploring efficiently. In this paper, we propose an algorithm that addresses each of these challenges and is able to learn human-level policies on nearly all Atari games. A new transformed Bellman operator allows our algorithm to process rewards of varying densities and scales; an auxiliary temporal consistency loss allows us to train stably using a discount factor of $γ= 0.999$ (instead of $γ= 0.99$) extending the effective planning horizon by an order of magnitude; and we ease the exploration problem by using human demonstrations that guide the agent towards rewarding states. When tested on a set of 42 Atari games, our algorithm exceeds the performance of an average human on 40 games using a common set of hyper parameters. Furthermore, it is the first deep RL algorithm to solve the first level of Montezuma's Revenge.

Matteo Hessel, Joseph Modayil, Hado van Hasselt et al.

The deep reinforcement learning community has made several independent improvements to the DQN algorithm. However, it is unclear which of these extensions are complementary and can be fruitfully combined. This paper examines six extensions to the DQN algorithm and empirically studies their combination. Our experiments show that the combination provides state-of-the-art performance on the Atari 2600 benchmark, both in terms of data efficiency and final performance. We also provide results from a detailed ablation study that shows the contribution of each component to overall performance.

Meire Fortunato, Mohammad Gheshlaghi Azar, Bilal Piot et al.

We introduce NoisyNet, a deep reinforcement learning agent with parametric noise added to its weights, and show that the induced stochasticity of the agent's policy can be used to aid efficient exploration. The parameters of the noise are learned with gradient descent along with the remaining network weights. NoisyNet is straightforward to implement and adds little computational overhead. We find that replacing the conventional exploration heuristics for A3C, DQN and dueling agents (entropy reward and $ε$-greedy respectively) with NoisyNet yields substantially higher scores for a wide range of Atari games, in some cases advancing the agent from sub to super-human performance.

Audrunas Gruslys, Will Dabney, Mohammad Gheshlaghi Azar et al.

In this work we present a new agent architecture, called Reactor, which combines multiple algorithmic and architectural contributions to produce an agent with higher sample-efficiency than Prioritized Dueling DQN (Wang et al., 2016) and Categorical DQN (Bellemare et al., 2017), while giving better run-time performance than A3C (Mnih et al., 2016). Our first contribution is a new policy evaluation algorithm called Distributional Retrace, which brings multi-step off-policy updates to the distributional reinforcement learning setting. The same approach can be used to convert several classes of multi-step policy evaluation algorithms designed for expected value evaluation into distributional ones. Next, we introduce the \b{eta}-leave-one-out policy gradient algorithm which improves the trade-off between variance and bias by using action values as a baseline. Our final algorithmic contribution is a new prioritized replay algorithm for sequences, which exploits the temporal locality of neighboring observations for more efficient replay prioritization. Using the Atari 2600 benchmarks, we show that each of these innovations contribute to both the sample efficiency and final agent performance. Finally, we demonstrate that Reactor reaches state-of-the-art performance after 200 million frames and less than a day of training.

Todd Hester, Matej Vecerik, Olivier Pietquin et al.

Deep reinforcement learning (RL) has achieved several high profile successes in difficult decision-making problems. However, these algorithms typically require a huge amount of data before they reach reasonable performance. In fact, their performance during learning can be extremely poor. This may be acceptable for a simulator, but it severely limits the applicability of deep RL to many real-world tasks, where the agent must learn in the real environment. In this paper we study a setting where the agent may access data from previous control of the system. We present an algorithm, Deep Q-learning from Demonstrations (DQfD), that leverages small sets of demonstration data to massively accelerate the learning process even from relatively small amounts of demonstration data and is able to automatically assess the necessary ratio of demonstration data while learning thanks to a prioritized replay mechanism. DQfD works by combining temporal difference updates with supervised classification of the demonstrator's actions. We show that DQfD has better initial performance than Prioritized Dueling Double Deep Q-Networks (PDD DQN) as it starts with better scores on the first million steps on 41 of 42 games and on average it takes PDD DQN 83 million steps to catch up to DQfD's performance. DQfD learns to out-perform the best demonstration given in 14 of 42 games. In addition, DQfD leverages human demonstrations to achieve state-of-the-art results for 11 games. Finally, we show that DQfD performs better than three related algorithms for incorporating demonstration data into DQN.

Florian Strub, Harm de Vries, Jeremie Mary et al.

End-to-end design of dialogue systems has recently become a popular research topic thanks to powerful tools such as encoder-decoder architectures for sequence-to-sequence learning. Yet, most current approaches cast human-machine dialogue management as a supervised learning problem, aiming at predicting the next utterance of a participant given the full history of the dialogue. This vision is too simplistic to render the intrinsic planning problem inherent to dialogue as well as its grounded nature, making the context of a dialogue larger than the sole history. This is why only chit-chat and question answering tasks have been addressed so far using end-to-end architectures. In this paper, we introduce a Deep Reinforcement Learning method to optimize visually grounded task-oriented dialogues, based on the policy gradient algorithm. This approach is tested on a dataset of 120k dialogues collected through Mechanical Turk and provides encouraging results at solving both the problem of generating natural dialogues and the task of discovering a specific object in a complex picture.

Matthieu Geist, Bilal Piot, Olivier Pietquin

This paper aims at theoretically and empirically comparing two standard optimization criteria for Reinforcement Learning: i) maximization of the mean value and ii) minimization of the Bellman residual. For that purpose, we place ourselves in the framework of policy search algorithms, that are usually designed to maximize the mean value, and derive a method that minimizes the residual $\|T_* v_π- v_π\|_{1,ν}$ over policies. A theoretical analysis shows how good this proxy is to policy optimization, and notably that it is better than its value-based counterpart. We also propose experiments on randomly generated generic Markov decision processes, specifically designed for studying the influence of the involved concentrability coefficient. They show that the Bellman residual is generally a bad proxy to policy optimization and that directly maximizing the mean value is much better, despite the current lack of deep theoretical analysis. This might seem obvious, as directly addressing the problem of interest is usually better, but given the prevalence of (projected) Bellman residual minimization in value-based reinforcement learning, we believe that this question is worth to be considered.

Bilal Piot, Matthieu Geist, Olivier Pietquin

This paper reports applications of Difference of Convex functions (DC) programming to Learning from Demonstrations (LfD) and Reinforcement Learning (RL) with expert data. This is made possible because the norm of the Optimal Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is DC. Improvement in performance is demonstrated on two specific algorithms, namely Reward-regularized Classification for Apprenticeship Learning (RCAL) and Reinforcement Learning with Expert Demonstrations (RLED), through experiments on generic Markov Decision Processes (MDP), called Garnets.