arXiv subjects

Michal Valko

Publications and source records attributed to Michal Valko.

At least 91 records · Page 5Linked to original sources

arXiv2023

Fast Rates for Maximum Entropy Exploration

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.

stat.ML↗

arXiv2023

DoMo-AC: Doubly Multi-step Off-policy Actor-Critic Algorithm

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

cs.LG↗

arXiv2023

Regularization and Variance-Weighted Regression Achieves Minimax Optimality in Linear MDPs: Theory and Practice

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an $\varepsilon$-optimal policy with probability $1-δ$ under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

cs.LG↗

arXiv2023

Unlocking the Power of Representations in Long-term Novelty-based Exploration

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!".

cs.LG↗

arXiv2023

Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

math.PR↗

arXiv2023

Large-Scale Representation Learning on Graphs via Bootstrapping

Self-supervised learning provides a promising path towards eliminating the need for costly label information in representation learning on graphs. However, to achieve state-of-the-art performance, methods often need large numbers of negative examples and rely on complex augmentations. This can be prohibitively expensive, especially for large graphs. To address these challenges, we introduce Bootstrapped Graph Latents (BGRL) - a graph representation learning method that learns by predicting alternative augmentations of the input. BGRL uses only simple augmentations and alleviates the need for contrasting with negative examples, and is thus scalable by design. BGRL outperforms or matches prior methods on several established benchmarks, while achieving a 2-10x reduction in memory costs. Furthermore, we show that BGRL can be scaled up to extremely large graphs with hundreds of millions of nodes in the semi-supervised regime - achieving state-of-the-art performance and improving over supervised baselines where representations are shaped only through label information. In particular, our solution centered on BGRL constituted one of the winning entries to the Open Graph Benchmark - Large Scale Challenge at KDD Cup 2021, on a graph orders of magnitudes larger than all previously available benchmarks, thus demonstrating the scalability and effectiveness of our approach.

cs.LG↗

arXiv2023

Adapting to game trees in zero-sum imperfect information games

Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $ε$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\widetilde{\mathcal{O}}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/ε^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ and $B_{\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs $\widetilde{\mathcal{O}}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/ε^2)$ realizations without this requirement by progressively adapting the regularization to the observations.

stat.ML↗

arXiv2022

Understanding Self-Predictive Learning for Reinforcement Learning

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.

cs.LG↗

arXiv2022

Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guarantees

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon $H$ with $S$ states, and $A$ actions. The performance of an agent is measured by the regret after interacting with the environment for $T$ episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in $H$, $S$, $A$, and $T$ per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most $\widetilde{\mathcal{O}}(\sqrt{H^3SAT})$ ignoring $\text{poly}\log(HSAT)$ terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges [1984] to Dirichlet distributions. Our bound matches the lower bound of order $Ω(\sqrt{H^3SAT})$, thereby answering the open problems raised by Agrawal and Jia [2017b] for the episodic setting.

stat.ML↗

arXiv2022

On the Approximation Relationship between Optimizing Ratio of Submodular (RS) and Difference of Submodular (DS) Functions

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical one -- for the difference of submodular (DS) optimization problem, and vice versa. We also illustrate the link between these two problems by analyzing a \textsc{Greedy} algorithm which approximately maximizes objective functions of the form $Ψ(f,g)$, where $f,g$ are two non-negative, monotone, submodular functions and $Ψ$ is a {quasiconvex} 2-variables function, which is non decreasing with respect to the first variable. For the choice $Ψ(f,g)\triangleq f/g$, we recover RS, and for the choice $Ψ(f,g)\triangleq f-g$, we recover DS. To the best of our knowledge, this greedy approach is new for DS optimization. For RS optimization, it reduces to the standard \textsc{GreedRatio} algorithm that has already been analyzed previously. However, our analysis is novel for this case.

cs.DS↗

arXiv2022

From Dirichlet to Rubin: Optimistic Exploration in RL without Bonuses

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order $\widetilde{O}(\sqrt{H^3SAT})$ where $H$ is the length of one episode, $S$ is the number of states, $A$ the number of actions, $T$ the number of episodes, that matches the lower-bound of $Ω(\sqrt{H^3SAT})$ up to poly-$\log$ terms in $H,S,A,T$ for a large enough $T$. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon $H$ (and $S$) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

stat.ML↗

arXiv2022

BYOL-Explore: Exploration by Bootstrapped Prediction

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.

cs.LG↗

arXiv2022

KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal

In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an $\varepsilon$-optimal policy when $\varepsilon$ is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.

cs.LG↗

arXiv2022

Retrieval-Augmented Reinforcement Learning

Most deep reinforcement learning (RL) algorithms distill experience into parametric behavior policies or value functions via gradient updates. While effective, this approach has several disadvantages: (1) it is computationally expensive, (2) it can take many updates to integrate experiences into the parametric model, (3) experiences that are not fully integrated do not appropriately influence the agent's behavior, and (4) behavior is limited by the capacity of the model. In this paper we explore an alternative paradigm in which we train a network to map a dataset of past experiences to optimal behavior. Specifically, we augment an RL agent with a retrieval process (parameterized as a neural network) that has direct access to a dataset of experiences. This dataset can come from the agent's past experiences, expert demonstrations, or any other relevant source. The retrieval process is trained to retrieve information from the dataset that may be useful in the current context, to help the agent achieve its goal faster and more efficiently. he proposed method facilitates learning agents that at test-time can condition their behavior on the entire dataset and not only the current state, or current trajectory. We integrate our method into two different RL agents: an offline DQN agent and an online R2D2 agent. In offline multi-task problems, we show that the retrieval-augmented DQN agent avoids task interference and learns faster than the baseline DQN agent. On Atari, we show that retrieval-augmented R2D2 learns significantly faster than the baseline R2D2 agent and achieves higher scores. We run extensive ablations to measure the contributions of the components of our proposed method.

cs.LG↗

arXiv2022

Marginalized Operators for Off-policy Reinforcement Learning

In this work, we propose marginalized operators, a new class of off-policy evaluation operators for reinforcement learning. Marginalized operators strictly generalize generic multi-step operators, such as Retrace, as special cases. Marginalized operators also suggest a form of sample-based estimates with potential variance reduction, compared to sample-based estimates of the original multi-step operators. We show that the estimates for marginalized operators can be computed in a scalable way, which also generalizes prior results on marginalized importance sampling as special cases. Finally, we empirically demonstrate that marginalized operators provide performance gains to off-policy evaluation and downstream policy optimization algorithms.

cs.LG↗

arXiv2022

Kernel-Based Reinforcement Learning: A Finite-Time Analysis

We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning problems whose state-action space is endowed with a metric. We introduce Kernel-UCBVI, a model-based optimistic algorithm that leverages the smoothness of the MDP and a non-parametric kernel estimator of the rewards and transitions to efficiently balance exploration and exploitation. For problems with $K$ episodes and horizon $H$, we provide a regret bound of $\widetilde{O}\left( H^3 K^{\frac{2d}{2d+1}}\right)$, where $d$ is the covering dimension of the joint state-action space. This is the first regret bound for kernel-based RL using smoothing kernels, which requires very weak assumptions on the MDP and has been previously applied to a wide range of tasks. We empirically validate our approach in continuous MDPs with sparse rewards.

cs.LG↗

arXiv2022

A Kernel-Based Approach to Non-Stationary Reinforcement Learning in Metric Spaces

In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a practical implementation of KeRNS, we analyze its regret and validate it experimentally.

cs.LG↗

arXiv2022

UCB Momentum Q-learning: Correcting the bias without forgetting

We propose UCBMQ, Upper Confidence Bound Momentum Q-learning, a new algorithm for reinforcement learning in tabular and possibly stage-dependent, episodic Markov decision process. UCBMQ is based on Q-learning where we add a momentum term and rely on the principle of optimism in face of uncertainty to deal with exploration. Our new technical ingredient of UCBMQ is the use of momentum to correct the bias that Q-learning suffers while, at the same time, limiting the impact it has on the second-order term of the regret. For UCBMQ, we are able to guarantee a regret of at most $O(\sqrt{H^3SAT}+ H^4 S A )$ where $H$ is the length of an episode, $S$ the number of states, $A$ the number of actions, $T$ the number of episodes and ignoring terms in poly-$\log(SAHT)$. Notably, UCBMQ is the first algorithm that simultaneously matches the lower bound of $Ω(\sqrt{H^3SAT})$ for large enough $T$ and has a second-order term (with respect to the horizon $T$) that scales only linearly with the number of states $S$.

stat.ML↗