arXiv subjects

Kaito Ariu

Publications and source records attributed to Kaito Ariu.

At least 19 recordsLinked to original sources

arXiv2026

Linear Convergence in Games with Delayed Feedback via Extra Prediction

Feedback delays are inevitable in real-world multi-agent learning. They are known to severely degrade performance, and the convergence rate under delayed feedback is still unclear, even for bilinear games. This paper derives the rate of linear convergence of Weighted Optimistic Gradient Descent-Ascent (WOGDA), which predicts future rewards with extra optimism, in unconstrained bilinear games. To analyze the algorithm, we interpret it as an approximation of the Extra Proximal Point (EPP), which is updated based on farther future rewards than the classical Proximal Point (PP). Our theorems show that standard optimism (predicting the next-step reward) achieves linear convergence to the equilibrium at a rate $\exp(-\Theta(t/m^{5}))$ after $t$ iterations for delay $m$. Moreover, employing extra optimism (predicting farther future reward) tolerates a larger step size and significantly accelerates the rate to $\exp(-\Theta(t/(m^{2}\log m)))$. Our experiments also show accelerated convergence driven by the extra optimism and are qualitatively consistent with our theorems. In summary, this paper validates that extra optimism is a promising countermeasure against performance degradation caused by feedback delays.

cs.LG↗

arXiv2026

Consensus Group Relative Policy Optimization for Text Generation

Many strong decoding methods for text generation follow a sample-and-rerank paradigm: they draw multiple candidates, score each under a utility (reward) function using consensus across samples, and return the best one. Although effective, these methods incur high computational costs during inference due to repeated sampling and scoring. Prior attempts to amortize inference-time computation typically rely on gold references, teacher labels, or curated preference data, increasing dataset construction effort and the demand for high-fidelity reward models. We propose Consensus Group Relative Policy Optimization (C-GRPO), which distills Minimum Bayes Risk (MBR) decoding into training by formulating the consensus utility as a group-relative objective within GRPO. C-GRPO requires only a utility function and policy samples, without gold references or explicit preference labels. Under ideal conditions, we show that the objective function of C-GRPO is directionally aligned with the gradient of the expected-utility objective underlying MBR decoding, leading to a convergence guarantee. Experiments on machine translation (WMT 2024) and text summarization (XSum) demonstrate that C-GRPO successfully achieves performance comparable to MBR decoding without the associated inference-time overhead, while outperforming reference-free baseline methods.

cs.LG↗

arXiv2026

What you reward is what you learn: Comparing rewards for online speech policy optimization in public HRI

Designing policies that are both efficient and acceptable for conversational service robots in open and diverse environments is non-trivial. Unlike fixed, hand-tuned parameters, online learning can adapt to non-stationary conditions. In this paper, we study how to adapt a social robot's speech policy in the wild. During a 12-day in-situ deployment with over 1,400 public encounters, we cast online policy optimization as a multi-armed bandit problem and use Thompson sampling to select among six actions defined by speech rate (slow/normal/fast) and verbosity (concise/detailed). We compare three complementary binary rewards--Ru (user rating), Rc (conversation closure), and Rt (>=2 turns)--and show that each induces distinct arm distributions and interaction behaviors. We complement the online results with offline evaluations that analyze contextual factors (e.g., crowd level, group size) using video-annotated data. Taken together, we distill ready-to-use design lessons for deploying online optimization of speech policies in real public HRI settings.

cs.RO↗

arXiv2025

Learning from Delayed Feedback in Games via Extra Prediction

This study raises and addresses the problem of time-delayed feedback in learning in games. Because learning in games assumes that multiple agents independently learn their strategies, a discrepancy in optimization often emerges among the agents. To overcome this discrepancy, the prediction of the future reward is incorporated into algorithms, typically known as Optimistic Follow-the-Regularized-Leader (OFTRL). However, the time delay in observing the past rewards hinders the prediction. Indeed, this study firstly proves that even a single-step delay worsens the performance of OFTRL from the aspects of social regret and convergence. This study proposes the weighted OFTRL (WOFTRL), where the prediction vector of the next reward in OFTRL is weighted $n$ times. We further capture an intuition that the optimistic weight cancels out this time delay. We prove that when the optimistic weight exceeds the time delay, our WOFTRL recovers the good performances that social regret is constant in general-sum normal-form games, and the strategies last-iterate converge to the Nash equilibrium in poly-matrix zero-sum games. The theoretical results are supported and strengthened by our experiments.

cs.LG↗

arXiv2025

Last Iterate Convergence in Monotone Mean Field Games

In the Lasry--Lions framework, Mean-Field Games (MFGs) model interactions among an infinite number of agents. However, existing algorithms either require strict monotonicity or only guarantee the convergence of averaged iterates, as in Fictitious Play in continuous time. We address this gap with the following theoretical result. First, we prove that the last-iterated policy of a proximal-point (PP) update with KL regularization converges to an equilibrium of MFG under non-strict monotonicity. Second, we see that each PP update is equivalent to finding the equilibria of a KL-regularized MFG. We then prove that this equilibrium can be found using Mirror Descent (MD) with an exponential last-iterate convergence rate. Building on these insights, we propose the Approximate Proximal-Point ($\mathtt{APP}$) algorithm, which approximately implements the PP update via a small number of MD steps. Numerical experiments on standard benchmarks confirm that the $\mathtt{APP}$ algorithm reliably converges to the unregularized mean-field equilibrium without time-averaging.

cs.GT↗

arXiv2025

Revisiting Instance-Optimal Cluster Recovery in the Labeled Stochastic Block Model

In this paper, we investigate the problem of recovering hidden communities in the Labeled Stochastic Block Model (LSBM) with a finite number of clusters whose sizes grow linearly with the total number of nodes. We derive the necessary and sufficient conditions under which the expected number of misclassified nodes is less than $ s $, for any number $ s = o(n) $. To achieve this, we propose IAC (Instance-Adaptive Clustering), the first algorithm whose performance matches the instance-specific lower bounds both in expectation and with high probability. IAC is a novel two-phase algorithm that consists of a one-shot spectral clustering step followed by iterative likelihood-based cluster assignment improvements. This approach is based on the instance-specific lower bound and notably does not require any knowledge of the model parameters, including the number of clusters. By performing the spectral clustering only once, IAC maintains an overall computational complexity of $ \mathcal{O}(n\, \text{polylog}(n)) $, making it scalable and practical for large-scale problems.

cs.SI↗

arXiv2025

On the Power of Perturbation under Sampling in Solving Extensive-Form Games

We investigate how perturbation does and does not improve the Follow-the-Regularized-Leader (FTRL) algorithm in solving imperfect-information extensive-form games under sampling, where payoffs are estimated from sampled trajectories. While optimistic algorithms are effective under full feedback, they often become unstable in the presence of sampling noise. Payoff perturbation offers a promising alternative for stabilizing learning and achieving \textit{last-iterate convergence}. We present a unified framework for \textit{Perturbed FTRL} algorithms and study two variants: PFTRL-KL (standard KL divergence) and PFTRL-RKL (Reverse KL divergence), the latter featuring an estimator with both unbiasedness and conditional zero variance. While PFTRL-KL generally achieves equivalent or better performance across benchmark games, PFTRL-RKL consistently outperforms it in Leduc poker, whose structure is more asymmetric than the other games in a sense. Given the modest advantage of PFTRL-RKL, we design the second experiment to isolate the effect of conditional zero variance, showing that the variance-reduction property of RKL improve last-iterate performance.

cs.GT↗

arXiv2025

Theoretical Guarantees for Minimum Bayes Risk Decoding

Minimum Bayes Risk (MBR) decoding optimizes output selection by maximizing the expected utility value of an underlying human distribution. While prior work has shown the effectiveness of MBR decoding through empirical evaluation, few studies have analytically investigated why the method is effective. As a result of our analysis, we show that, given the size $n$ of the reference hypothesis set used in computation, MBR decoding approaches the optimal solution with high probability at a rate of $O\left(n^{-\frac{1}{2}}\right)$, under certain assumptions, even though the language space $Y$ is significantly larger $|Y|\gg n$. This result helps to theoretically explain the strong performance observed in several prior empirical studies on MBR decoding. In addition, we provide the performance gap for maximum-a-posteriori (MAP) decoding and compare it to MBR decoding. The result of this paper indicates that MBR decoding tends to converge to the optimal solution faster than MAP decoding in several cases.

cs.CL↗

arXiv2025

Return-Aligned Decision Transformer

Traditional approaches in offline reinforcement learning aim to learn the optimal policy that maximizes the cumulative reward, also known as return. It is increasingly important to adjust the performance of AI agents to meet human requirements, for example, in applications like video games and education tools. Decision Transformer (DT) optimizes a policy that generates actions conditioned on the target return through supervised learning and includes a mechanism to control the agent's performance using the target return. However, the action generation is hardly influenced by the target return because DT's self-attention allocates scarce attention scores to the return tokens. In this paper, we propose Return-Aligned Decision Transformer (RADT), designed to more effectively align the actual return with the target return. RADT leverages features extracted by paying attention solely to the return, enabling action generation to consistently depend on the target return. Extensive experiments show that RADT significantly reduces the discrepancies between the actual return and the target return compared to DT-based methods. Our code is available at https://github.com/CyberAgentAILab/radt

cs.LG↗

arXiv2025

Asymmetric Perturbation in Solving Bilinear Saddle-Point Optimization

This paper proposes asymmetric perturbation, where only one player's payoff function is perturbed, for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Symmetric perturbation is known to require decreasing its strength to ensure convergence to a solution, i.e., an equilibrium in the original game, resulting in a slower rate. First, with asymmetric perturbation, we show that, for a sufficiently small perturbation strength, the equilibrium strategy of the asymmetrically perturbed game coincides with an equilibrium strategy of the original unperturbed game. Second, building on this coincidence, we construct a learning algorithm with a linear last-iterate convergence rate. Third, motivated by the fact that the coincidence relies on the perturbation strength being sufficiently small, we also provide a parameter-free variant, retaining the linear rate. Finally, we empirically demonstrate fast convergence toward equilibria in both normal-form and extensive-form games.

math.OC↗

arXiv2025

Policy Testing in Markov Decision Processes

We study the policy testing problem in discounted Markov decision processes (MDPs) in the fixed-confidence setting under a generative model with static sampling. The goal is to decide whether the value of a given policy exceeds a specified threshold while minimizing the number of samples. We first derive an instance-dependent lower bound that any reasonable algorithm must satisfy, characterized as the solution to an optimization problem with non-convex constraints. Guided by this formulation, we propose a new algorithm. While this design paradigm is common in pure exploration problems such as best-arm identification, the non-convex constraints that arise in MDPs introduce substantial difficulties. To address them, we reformulate the lower-bound problem by swapping the roles of the objective and the constraints, yielding an alternative problem with a non-convex objective but convex constraints. This reformulation admits an interpretation as a policy optimization task in a newly constructed reversed MDP. We further show that the global KL constraint can be decomposed exactly into a family of product-box subproblems, which are solved by projected policy gradient and combined through an outer budget search. Beyond policy testing, our reformulation and reversed MDP view suggest extensions to other pure exploration tasks in MDPs, including policy evaluation and best policy identification.

stat.ML↗

arXiv2025

Nash Equilibrium and Learning Dynamics in Three-Player Matching $m$-Action Games

Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their benefits are competitive, have already been well analyzed. However, it is still unexplored and challenging to analyze the dynamics of learning among three players. In this study, we formulate a minimalistic game where three players compete to match their actions with one another. Although interaction among three players diversifies and complicates the Nash equilibria, we fully analyze the equilibria. We also discuss the dynamics of learning based on some famous algorithms categorized into Follow the Regularized Leader. From both theoretical and experimental aspects, we characterize the dynamics by categorizing three-player interactions into three forces to synchronize their actions, switch their actions rotationally, and seek competition.

cs.GT↗

arXiv2025

Global Behavior of Learning Dynamics in Zero-Sum Games with Memory Asymmetry

This study examines the global behavior of dynamics in learning in games between two players, X and Y. We consider the simplest situation for memory asymmetry between two players: X memorizes the other Y's previous action and uses reactive strategies, while Y has no memory. Although this memory complicates their learning dynamics, we characterize the global behavior of such complex dynamics by discovering and analyzing two novel quantities. One is an extended Kullback-Leibler divergence from the Nash equilibrium, a well-known conserved quantity from previous studies. The other is a family of Lyapunov functions of X's reactive strategy. One of the global behaviors we capture is that if X exploits Y, then their strategies converge to the Nash equilibrium. Another is that if Y's strategy is out of equilibrium, then X becomes more exploitative with time. Consequently, we suggest global convergence to the Nash equilibrium from both aspects of theory and experiment. This study provides a novel characterization of the global behavior in learning in games through a couple of indicators.

cs.GT↗

arXiv2025

Synchronization in Learning in Periodic Zero-Sum Games Triggers Divergence from Nash Equilibrium

Learning in zero-sum games studies a situation where multiple agents competitively learn their strategy. In such multi-agent learning, we often see that the strategies cycle around their optimum, i.e., Nash equilibrium. When a game periodically varies (called a ``periodic'' game), however, the Nash equilibrium moves generically. How learning dynamics behave in such periodic games is of interest but still unclear. Interestingly, we discover that the behavior is highly dependent on the relationship between the two speeds at which the game changes and at which players learn. We observe that when these two speeds synchronize, the learning dynamics diverge, and their time-average does not converge. Otherwise, the learning dynamics draw complicated cycles, but their time-average converges. Under some assumptions introduced for the dynamical systems analysis, we prove that this behavior occurs. Furthermore, our experiments observe this behavior even if removing these assumptions. This study discovers a novel phenomenon, i.e., synchronization, and gains insight widely applicable to learning in periodic games.

cs.GT↗

arXiv2025

Boosting Perturbed Gradient Ascent for Last-Iterate Convergence in Games

This paper presents a payoff perturbation technique, introducing a strong convexity to players' payoff functions in games. This technique is specifically designed for first-order methods to achieve last-iterate convergence in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. Although perturbation is known to facilitate the convergence of learning algorithms, the magnitude of perturbation requires careful adjustment to ensure last-iterate convergence. Previous studies have proposed a scheme in which the magnitude is determined by the distance from a periodically re-initialized anchoring or reference strategy. Building upon this, we propose Gradient Ascent with Boosting Payoff Perturbation, which incorporates a novel perturbation into the underlying payoff function, maintaining the periodically re-initializing anchoring strategy scheme. This innovation empowers us to provide faster last-iterate convergence rates against the existing payoff perturbed algorithms, even in the presence of additive noise.

cs.GT↗

arXiv2025

Evaluation of Best-of-N Sampling Strategies for Language Model Alignment

Best-of-N (BoN) sampling with a reward model has been shown to be an effective strategy for aligning Large Language Models (LLMs) with human preferences at the time of decoding. BoN sampling is susceptible to a problem known as reward hacking. Since the reward model is an imperfect proxy for the true objective, an excessive focus on optimizing its value can lead to a compromise of its performance on the true objective. Previous work proposes Regularized BoN sampling (RBoN), a BoN sampling with regularization to the objective, and shows that it outperforms BoN sampling so that it mitigates reward hacking and empirically (Jinnai et al., 2024). However, Jinnai et al. (2024) introduce RBoN based on a heuristic and they lack the analysis of why such regularization strategy improves the performance of BoN sampling. The aim of this study is to analyze the effect of BoN sampling on regularization strategies. Using the regularization strategies corresponds to robust optimization, which maximizes the worst case over a set of possible perturbations in the proxy reward. Although the theoretical guarantees are not directly applicable to RBoN, RBoN corresponds to a practical implementation. This paper proposes an extension of the RBoN framework, called Stochastic RBoN sampling (SRBoN), which is a theoretically guaranteed approach to worst-case RBoN in proxy reward. We then perform an empirical evaluation using the AlpacaFarm and Anthropic's hh-rlhf datasets to evaluate which factors of the regularization strategies contribute to the improvement of the true proxy reward. In addition, we also propose another simple RBoN method, the Sentence Length Regularized BoN, which has a better performance in the experiment as compared to the previous methods.

cs.CL↗

arXiv2025

Regularized Best-of-N Sampling with Minimum Bayes Risk Objective for Language Model Alignment

Best-of-N (BoN) sampling with a reward model has been shown to be an effective strategy for aligning Large Language Models (LLMs) to human preferences at the time of decoding. BoN sampling is susceptible to a problem known as reward hacking when the accuracy of the reward model is not high enough due to the quality or the quantity of the preference dataset. Because the reward model is an imperfect proxy for the true objective, over-optimizing its value can compromise its performance on the true objective. In this research, we propose MBR-BoN, a variant of BoN that aims to mitigate reward hacking at inference time by incorporating the Minimum Bayes Risk (MBR) objective as a proximity regularization term. We show empirically and analytically that the MBR objective quantifies the proximity of the response to the reference policy, serving as a proximity regularizer. We evaluate MBR-BoN on the AlpacaFarm and Anthropic's hh-rlhf datasets and show that it outperforms both BoN sampling and MBR decoding. We also evaluate MBR-BoN to generate a pairwise preference learning dataset for Direct Preference Optimization (DPO). Empirical results show that models trained on a dataset generated with MBR-BoN outperform those with vanilla BoN. Our code is available at https://github.com/CyberAgentAILab/regularized-bon

cs.CL↗

arXiv2024

Filtered Direct Preference Optimization

Reinforcement learning from human feedback (RLHF) plays a crucial role in aligning language models with human preferences. While the significance of dataset quality is generally recognized, explicit investigations into its impact within the RLHF framework, to our knowledge, have been limited. This paper addresses the issue of text quality within the preference dataset by focusing on direct preference optimization (DPO), an increasingly adopted reward-model-free RLHF method. We confirm that text quality significantly influences the performance of models optimized with DPO more than those optimized with reward-model-based RLHF. Building on this new insight, we propose an extension of DPO, termed filtered direct preference optimization (fDPO). fDPO uses a trained reward model to monitor the quality of texts within the preference dataset during DPO training. Samples of lower quality are discarded based on comparisons with texts generated by the model being optimized, resulting in a more accurate dataset. Experimental results demonstrate that fDPO enhances the final model performance. Our code is available at https://github.com/CyberAgentAILab/filtered-dpo.

cs.LG↗