Toshinori Kitamura

Tadashi Kozuno, Wenhao Yang, Nino Vieillard et al. · deepmind

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.

Soichiro Nishimori, Paavo Parmas, Sotetsu Koyamada et al.

In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over $M$ samples, where $M$ is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count $M$ to a continuous parameter $m > 0$, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks.

Kushagra Chandak, Toshinori Kitamura, Xiaoqi Tan

We study online learning with an additional offline dataset in the stochastic linear bandit setting. Although this problem arises frequently in practice, the offline-to-online tradeoff remains poorly understood in structured environments. We propose a linear bandit algorithm that balances this tradeoff: it relies on offline data during early rounds, and increasingly favors exploration as the horizon grows. We establish regret bounds showing that our method is simultaneously competitive with both purely online and purely offline solutions. In particular, it achieves sublinear regret relative to the optimal action in the number of online interactions, while its regret relative to an offline reference decreases as the number of offline samples grows. Empirical results further demonstrate its effectiveness across various problem parameters.

Toshinori Kitamura, Tadashi Kozuno, Wataru Kumagai et al.

Designing a safe policy for uncertain environments is crucial in real-world control systems. However, this challenge remains inadequately addressed within the Markov decision process (MDP) framework. This paper presents the first algorithm guaranteed to identify a near-optimal policy in a robust constrained MDP (RCMDP), where an optimal policy minimizes cumulative cost while satisfying constraints in the worst-case scenario across a set of environments. We first prove that the conventional policy gradient approach to the Lagrangian max-min formulation can become trapped in suboptimal solutions. This occurs when its inner minimization encounters a sum of conflicting gradients from the objective and constraint functions. To address this, we leverage the epigraph form of the RCMDP problem, which resolves the conflict by selecting a single gradient from either the objective or the constraints. Building on the epigraph form, we propose a bisection search algorithm with a policy gradient subroutine and prove that it identifies an $\varepsilon$-optimal policy in an RCMDP with $\tilde{\mathcal{O}}(\varepsilon^{-4})$ robust policy evaluations.

Toshinori Kitamura, Ryo Yonetani

We present ShinRL, an open-source library specialized for the evaluation of reinforcement learning (RL) algorithms from both theoretical and practical perspectives. Existing RL libraries typically allow users to evaluate practical performances of deep RL algorithms through returns. Nevertheless, these libraries are not necessarily useful for analyzing if the algorithms perform as theoretically expected, such as if Q learning really achieves the optimal Q function. In contrast, ShinRL provides an RL environment interface that can compute metrics for delving into the behaviors of RL algorithms, such as the gap between learned and the optimal Q values and state visitation frequencies. In addition, we introduce a flexible solver interface for evaluating both theoretically justified algorithms (e.g., dynamic programming and tabular RL) and practically effective ones (i.e., deep RL, typically with some additional extensions and regularizations) in a consistent fashion. As a case study, we show that how combining these two features of ShinRL makes it easier to analyze the behavior of deep Q learning. Furthermore, we demonstrate that ShinRL can be used to empirically validate recent theoretical findings such as the effect of KL regularization for value iteration and for deep Q learning, and the robustness of entropy-regularized policies to adversarial rewards. The source code for ShinRL is available on GitHub: https://github.com/omron-sinicx/ShinRL.

Toshinori Kitamura, Tadashi Kozuno, Masahiro Kato et al.

We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms for this problem only provides sublinear regret guarantees and fails to ensure convergence to optimal policies. In this paper, we introduce a novel policy gradient PD algorithm with uniform probably approximate correctness (Uniform-PAC) guarantees, simultaneously ensuring convergence to optimal policies, sublinear regret, and polynomial sample complexity for any target accuracy. Notably, this represents the first Uniform-PAC algorithm for the online CMDP problem. In addition to the theoretical guarantees, we empirically demonstrate in a simple CMDP that our algorithm converges to optimal policies, while baseline algorithms exhibit oscillatory performance and constraint violation.

Takeshi Kojima, Yaonan Zhu, Yusuke Iwasawa et al.

Recent Foundation Model-enabled robotics (FMRs) display greatly improved general-purpose skills, enabling more adaptable automation than conventional robotics. Their ability to handle diverse tasks thus creates new opportunities to replace human labor. However, unlike general foundation models, FMRs interact with the physical world, where their actions directly affect the safety of humans and surrounding objects, requiring careful deployment and control. Based on this proposition, our survey comprehensively summarizes robot control approaches to mitigate physical risks by covering all the lifespan of FMRs ranging from pre-deployment to post-accident stage. Specifically, we broadly divide the timeline into the following three phases: (1) pre-deployment phase, (2) pre-incident phase, and (3) post-incident phase. Throughout this survey, we find that there is much room to study (i) pre-incident risk mitigation strategies, (ii) research that assumes physical interaction with humans, and (iii) essential issues of foundation models themselves. We hope that this survey will be a milestone in providing a high-resolution analysis of the physical risks of FMRs and their control, contributing to the realization of a good human-robot relationship.

Toshinori Kitamura, Arnob Ghosh, Tadashi Kozuno et al.

We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total utility value in every episode. While this problem is well understood in the tabular setting, theoretical results for function approximation remain scarce. This paper closes the gap by proposing an RL algorithm for linear CMDPs that achieves $\tilde{\mathcal{O}}(\sqrt{K})$ regret with an episode-wise zero-violation guarantee. Furthermore, our method is computationally efficient, scaling polynomially with problem-dependent parameters while remaining independent of the state space size. Our results significantly improve upon recent linear CMDP algorithms, which either violate the constraint or incur exponential computational costs.

Toshinori Kitamura, Tadashi Kozuno, Yunhao Tang et al.

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.

Toshinori Kitamura, Lingwei Zhu, Takamitsu Matsubara

The recent boom in the literature on entropy-regularized reinforcement learning (RL) approaches reveals that Kullback-Leibler (KL) regularization brings advantages to RL algorithms by canceling out errors under mild assumptions. However, existing analyses focus on fixed regularization with a constant weighting coefficient and do not consider cases where the coefficient is allowed to change dynamically. In this paper, we study the dynamic coefficient scheme and present the first asymptotic error bound. Based on the dynamic coefficient error bound, we propose an effective scheme to tune the coefficient according to the magnitude of error in favor of more robust learning. Complementing this development, we propose a novel algorithm, Geometric Value Iteration (GVI), that features a dynamic error-aware KL coefficient design with the aim of mitigating the impact of errors on performance. Our experiments demonstrate that GVI can effectively exploit the trade-off between learning speed and robustness over uniform averaging of a constant KL coefficient. The combination of GVI and deep networks shows stable learning behavior even in the absence of a target network, where algorithms with a constant KL coefficient would greatly oscillate or even fail to converge.

Lingwei Zhu, Toshinori Kitamura, Takamitsu Matsubara

In this paper, we propose cautious policy programming (CPP), a novel value-based reinforcement learning (RL) algorithm that can ensure monotonic policy improvement during learning. Based on the nature of entropy-regularized RL, we derive a new entropy regularization-aware lower bound of policy improvement that only requires estimating the expected policy advantage function. CPP leverages this lower bound as a criterion for adjusting the degree of a policy update for alleviating policy oscillation. Different from similar algorithms that are mostly theory-oriented, we also propose a novel interpolation scheme that makes CPP better scale in high dimensional control problems. We demonstrate that the proposed algorithm can trade o? performance and stability in both didactic classic control problems and challenging high-dimensional Atari games.

Lingwei Zhu, Toshinori Kitamura, Takamitsu Matsubara

The oscillating performance of off-policy learning and persisting errors in the actor-critic (AC) setting call for algorithms that can conservatively learn to suit the stability-critical applications better. In this paper, we propose a novel off-policy AC algorithm cautious actor-critic (CAC). The name cautious comes from the doubly conservative nature that we exploit the classic policy interpolation from conservative policy iteration for the actor and the entropy-regularization of conservative value iteration for the critic. Our key observation is the entropy-regularized critic facilitates and simplifies the unwieldy interpolated actor update while still ensuring robust policy improvement. We compare CAC to state-of-the-art AC methods on a set of challenging continuous control problems and demonstrate that CAC achieves comparable performance while significantly stabilizes learning.