arXiv subjects

Tadashi Kozuno

Publications and source records attributed to Tadashi Kozuno.

36 records · Page 2Linked to original sources

arXiv2023

Local and adaptive mirror descents in extensive-form games

We study how to learn $ε$-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by $T$. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of $\tilde{\mathcal{O}}(T^{-1/2})$ with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

cs.GT↗

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

Benchmarking Actor-Critic Deep Reinforcement Learning Algorithms for Robotics Control with Action Constraints

This study presents a benchmark for evaluating action-constrained reinforcement learning (RL) algorithms. In action-constrained RL, each action taken by the learning system must comply with certain constraints. These constraints are crucial for ensuring the feasibility and safety of actions in real-world systems. We evaluate existing algorithms and their novel variants across multiple robotics control environments, encompassing multiple action constraint types. Our evaluation provides the first in-depth perspective of the field, revealing surprising insights, including the effectiveness of a straightforward baseline approach. The benchmark problems and associated code utilized in our experiments are made available online at github.com/omron-sinicx/action-constrained-RL-benchmark for further research and development.

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

Counterfactual Fairness Filter for Fair-Delay Multi-Robot Navigation

Multi-robot navigation is the task of finding trajectories for a team of robotic agents to reach their destinations as quickly as possible without collisions. In this work, we introduce a new problem: fair-delay multi-robot navigation, which aims not only to enable such efficient, safe travels but also to equalize the travel delays among agents in terms of actual trajectories as compared to the best possible trajectories. The learning of a navigation policy to achieve this objective requires resolving a nontrivial credit assignment problem with robotic agents having continuous action spaces. Hence, we developed a new algorithm called Navigation with Counterfactual Fairness Filter (NCF2). With NCF2, each agent performs counterfactual inference on whether it can advance toward its goal or should stay still to let other agents go. Doing so allows us to effectively address the aforementioned credit assignment problem and improve fairness regarding travel delays while maintaining high efficiency and safety. Our extensive experimental results in several challenging multi-robot navigation environments demonstrate the greater effectiveness of NCF2 as compared to state-of-the-art fairness-aware multi-agent reinforcement learning methods. Our demo videos and code are available on the project webpage: https://omron-sinicx.github.io/ncf2/

cs.MA↗

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

Confident Approximate Policy Iteration for Efficient Local Planning in $q^π$-realizable MDPs

We consider approximate dynamic programming in $γ$-discounted Markov decision processes and apply it to approximate planning with linear value-function approximation. Our first contribution is a new variant of Approximate Policy Iteration (API), called Confident Approximate Policy Iteration (CAPI), which computes a deterministic stationary policy with an optimal error bound scaling linearly with the product of the effective horizon $H$ and the worst-case approximation error $ε$ of the action-value functions of stationary policies. This improvement over API (whose error scales with $H^2$) comes at the price of an $H$-fold increase in memory cost. Unlike Scherrer and Lesner [2012], who recommended computing a non-stationary policy to achieve a similar improvement (with the same memory overhead), we are able to stick to stationary policies. This allows for our second contribution, the application of CAPI to planning with local access to a simulator and $d$-dimensional linear function approximation. As such, we design a planning algorithm that applies CAPI to obtain a sequence of policies with successively refined accuracies on a dynamically evolving set of states. The algorithm outputs an $\tilde O(\sqrt{d}Hε)$-optimal policy after issuing $\tilde O(dH^4/ε^2)$ queries to the simulator, simultaneously achieving the optimal accuracy bound and the best known query complexity bound, while earlier algorithms in the literature achieve only one of them. This query complexity is shown to be tight in all parameters except $H$. These improvements come at the expense of a mild (polynomial) increase in memory and computational costs of both the algorithm and its output policy.

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

No More Pesky Hyperparameters: Offline Hyperparameter Tuning for RL

The performance of reinforcement learning (RL) agents is sensitive to the choice of hyperparameters. In real-world settings like robotics or industrial control systems, however, testing different hyperparameter configurations directly on the environment can be financially prohibitive, dangerous, or time consuming. We propose a new approach to tune hyperparameters from offline logs of data, to fully specify the hyperparameters for an RL agent that learns online in the real world. The approach is conceptually simple: we first learn a model of the environment from the offline data, which we call a calibration model, and then simulate learning in the calibration model to identify promising hyperparameters. We identify several criteria to make this strategy effective, and develop an approach that satisfies these criteria. We empirically investigate the method in a variety of settings to identify when it is effective and when it fails.

cs.LG↗

arXiv2022

Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences

Approximate Policy Iteration (API) algorithms alternate between (approximate) policy evaluation and (approximate) greedification. Many different approaches have been explored for approximate policy evaluation, but less is understood about approximate greedification and what choices guarantee policy improvement. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. We show that the reverse KL has stronger policy improvement guarantees, but that reducing the forward KL can result in a worse policy. We also demonstrate, however, that a large enough reduction of the forward KL can induce improvement under additional assumptions. Empirically, we show on simple continuous-action environments that the forward KL can induce more exploration, but at the cost of a more suboptimal policy. No significant differences were observed in the discrete-action setting or on a suite of benchmark problems. Throughout, we highlight that many policy gradient methods can be seen as an instance of API, with either the forward or reverse KL for the policy update, and discuss next steps for understanding and improving our policy optimization algorithms.

cs.LG↗

arXiv2021

Unifying Gradient Estimators for Meta-Reinforcement Learning via Off-Policy Evaluation

Model-agnostic meta-reinforcement learning requires estimating the Hessian matrix of value functions. This is challenging from an implementation perspective, as repeatedly differentiating policy gradient estimates may lead to biased Hessian estimates. In this work, we provide a unifying framework for estimating higher-order derivatives of value functions, based on off-policy evaluation. Our framework interprets a number of prior approaches as special cases and elucidates the bias and variance trade-off of Hessian estimates. This framework also opens the door to a new family of estimates, which can be easily implemented with auto-differentiation libraries, and lead to performance gains in practice.

cs.LG↗

arXiv2021

Co-Adaptation of Algorithmic and Implementational Innovations in Inference-based Deep Reinforcement Learning

Recently many algorithms were devised for reinforcement learning (RL) with function approximation. While they have clear algorithmic distinctions, they also have many implementation differences that are algorithm-independent and sometimes under-emphasized. Such mixing of algorithmic novelty and implementation craftsmanship makes rigorous analyses of the sources of performance improvements across algorithms difficult. In this work, we focus on a series of off-policy inference-based actor-critic algorithms -- MPO, AWR, and SAC -- to decouple their algorithmic innovations and implementation decisions. We present unified derivations through a single control-as-inference objective, where we can categorize each algorithm as based on either Expectation-Maximization (EM) or direct Kullback-Leibler (KL) divergence minimization and treat the rest of specifications as implementation details. We performed extensive ablation studies, and identified substantial performance drops whenever implementation details are mismatched for algorithmic choices. These results show which implementation or code details are co-adapted and co-evolved with algorithms, and which are transferable across algorithms: as examples, we identified that tanh Gaussian policy and network sizes are highly adapted to algorithmic types, while layer normalization and ELU are critical for MPO's performances but also transfer to noticeable gains in SAC. We hope our work can inspire future work to further demystify sources of performance improvements across multiple algorithms and allow researchers to build on one another's both algorithmic and implementational innovations.

cs.LG↗

arXiv2021

Model-Free Learning for Two-Player Zero-Sum Partially Observable Markov Games with Perfect Recall

We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only feedback is realizations of the game (bandit feedback). In particular, the dynamic of the IIG is not known -- we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on the convergence rate to the NE of order $1/\sqrt{T}$ where $T$ is the number of played games. Moreover, IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.

stat.ML↗

arXiv2021

Policy Information Capacity: Information-Theoretic Measure for Task Complexity in Deep Reinforcement Learning

Progress in deep reinforcement learning (RL) research is largely enabled by benchmark task environments. However, analyzing the nature of those environments is often overlooked. In particular, we still do not have agreeable ways to measure the difficulty or solvability of a task, given that each has fundamentally different actions, observations, dynamics, rewards, and can be tackled with diverse RL algorithms. In this work, we propose policy information capacity (PIC) -- the mutual information between policy parameters and episodic return -- and policy-optimal information capacity (POIC) -- between policy parameters and episodic optimality -- as two environment-agnostic, algorithm-agnostic quantitative metrics for task difficulty. Evaluating our metrics across toy environments as well as continuous control benchmark tasks from OpenAI Gym and DeepMind Control Suite, we empirically demonstrate that these information-theoretic metrics have higher correlations with normalized task solvability scores than a variety of alternatives. Lastly, we show that these metrics can also be used for fast and compute-efficient optimizations of key design parameters such as reward shaping, policy architectures, and MDP properties for better solvability by RL algorithms without ever running full RL experiments.

cs.LG↗

arXiv2021

Revisiting Peng's Q($λ$) for Modern Reinforcement Learning

Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-function. In contrast, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. Motivated by the empirical results and the lack of theory, we carry out theoretical analyses of Peng's Q($λ$), a representative example of non-conservative algorithms. We prove that it also converges to an optimal policy provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result has been conjectured to be true but has not been proven. We also experiment with Peng's Q($λ$) in complex continuous control tasks, confirming that Peng's Q($λ$) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng's Q($λ$), which was thought to be unsafe, is a theoretically-sound and practically effective algorithm.

cs.LG↗

arXiv2021

Leverage the Average: an Analysis of KL Regularization in RL

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

cs.LG↗

arXiv2019

Gap-Increasing Policy Evaluation for Efficient and Noise-Tolerant Reinforcement Learning

In real-world applications of reinforcement learning (RL), noise from inherent stochasticity of environments is inevitable. However, current policy evaluation algorithms, which plays a key role in many RL algorithms, are either prone to noise or inefficient. To solve this issue, we introduce a novel policy evaluation algorithm, which we call Gap-increasing RetrAce Policy Evaluation (GRAPE). It leverages two recent ideas: (1) gap-increasing value update operators in advantage learning for noise-tolerance and (2) off-policy eligibility trace in Retrace algorithm for efficient learning. We provide detailed theoretical analysis of the new algorithm that shows its efficiency and noise-tolerance inherited from Retrace and advantage learning. Furthermore, our analysis shows that GRAPE's learning is significantly efficient than that of a simple learning-rate-based approach while keeping the same level of noise-tolerance. We applied GRAPE to control problems and obtained experimental results supporting our theoretical analysis.

cs.LG↗

arXiv2017

Unifying Value Iteration, Advantage Learning, and Dynamic Policy Programming

Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper we propose a new, robust dynamic programming algorithm that unifies value iteration, advantage learning, and dynamic policy programming. We call it generalized value iteration (GVI) and its approximated version, approximate GVI (AGVI). We show AGVI's performance guarantee, which includes performance guarantees for existing algorithms, as special cases. We discuss theoretical weaknesses of existing algorithms, and explain the advantages of AGVI. Numerical experiments in a simple environment support theoretical arguments, and suggest that AGVI is a promising alternative to previous algorithms.

stat.ML↗