Atsushi Iwasaki

Kenshi Abe, Mitsuki Sakamoto, Atsushi Iwasaki

In this study, we consider a variant of the Follow the Regularized Leader (FTRL) dynamics in two-player zero-sum games. FTRL is guaranteed to converge to a Nash equilibrium when time-averaging the strategies, while a lot of variants suffer from the issue of limit cycling behavior, i.e., lack the last-iterate convergence guarantee. To this end, we propose mutant FTRL (M-FTRL), an algorithm that introduces mutation for the perturbation of action probabilities. We then investigate the continuous-time dynamics of M-FTRL and provide the strong convergence guarantees toward stationary points that approximate Nash equilibria under full-information feedback. Furthermore, our simulation demonstrates that M-FTRL can enjoy faster convergence rates than FTRL and optimistic FTRL under full-information feedback and surprisingly exhibits clear convergence under bandit feedback.

Kenshi Abe, Kaito Ariu, Mitsuki Sakamoto et al.

This paper proposes Mutation-Driven Multiplicative Weights Update (M2WU) for learning an equilibrium in two-player zero-sum normal-form games and proves that it exhibits the last-iterate convergence property in both full and noisy feedback settings. In the former, players observe their exact gradient vectors of the utility functions. In the latter, they only observe the noisy gradient vectors. Even the celebrated Multiplicative Weights Update (MWU) and Optimistic MWU (OMWU) algorithms may not converge to a Nash equilibrium with noisy feedback. On the contrary, M2WU exhibits the last-iterate convergence to a stationary point near a Nash equilibrium in both feedback settings. We then prove that it converges to an exact Nash equilibrium by iteratively adapting the mutation term. We empirically confirm that M2WU outperforms MWU and OMWU in exploitability and convergence rates.

Hakuei Yamada, Junpei Komiyama, Kenshi Abe et al.

This work addresses learning online fair division under uncertainty, where a central planner sequentially allocates items without precise knowledge of agents' values or utilities. Departing from conventional online algorithm, the planner here relies on noisy, estimated values obtained after allocating items. We introduce wrapper algorithms utilizing \textit{dual averaging}, enabling gradual learning of both the type distribution of arriving items and agents' values through bandit feedback. This approach enables the algorithms to asymptotically achieve optimal Nash social welfare in linear Fisher markets with agents having additive utilities. We establish regret bounds in Nash social welfare and empirically validate the superior performance of our proposed algorithms across synthetic and empirical datasets.

Wataru Masaka, Mitsuki Sakamoto, Kenshi Abe et al.

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.

Hiroki Ishibashi, Kenshi Abe, Atsushi Iwasaki

This paper introduces state abstraction for two-player zero-sum Markov games (TZMGs), where the payoffs for the two players are determined by the state representing the environment and their respective actions, with state transitions following Markov decision processes. For example, in games like soccer, the value of actions changes according to the state of play, and thus such games should be described as Markov games. In TZMGs, as the number of states increases, computing equilibria becomes more difficult. Therefore, we consider state abstraction, which reduces the number of states by treating multiple different states as a single state. There is a substantial body of research on finding optimal policies for Markov decision processes using state abstraction. However, in the multi-player setting, the game with state abstraction may yield different equilibrium solutions from those of the ground game. To evaluate the equilibrium solutions of the game with state abstraction, we derived bounds on the duality gap, which represents the distance from the equilibrium solutions of the ground game. Finally, we demonstrate our state abstraction with Markov Soccer, compute equilibrium policies, and examine the results.

Kenshi Abe, Kaito Ariu, Mitsuki Sakamoto et al.

This paper proposes a payoff perturbation technique for the Mirror Descent (MD) algorithm in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. The optimistic family of learning algorithms, exemplified by optimistic MD, successfully achieves {\it last-iterate} convergence in scenarios devoid of noise, leading the dynamics to a Nash equilibrium. A recent re-emerging trend underscores the promise of the perturbation approach, where payoff functions are perturbed based on the distance from an anchoring, or {\it slingshot}, strategy. In response, we propose {\it Adaptively Perturbed MD} (APMD), which adjusts the magnitude of the perturbation by repeatedly updating the slingshot strategy at a predefined interval. This innovation empowers us to find a Nash equilibrium of the underlying game with guaranteed rates. Empirical demonstrations affirm that our algorithm exhibits significantly accelerated convergence.

Kenshi Abe, Junpei Komiyama, Atsushi Iwasaki

This paper considers the capacity expansion problem in two-sided matchings, where the policymaker is allowed to allocate some extra seats as well as the standard seats. In medical residency match, each hospital accepts a limited number of doctors. Such capacity constraints are typically given in advance. However, such exogenous constraints can compromise the welfare of the doctors; some popular hospitals inevitably dismiss some of their favorite doctors. Meanwhile, it is often the case that the hospitals are also benefited to accept a few extra doctors. To tackle the problem, we propose an anytime method that the upper confidence tree searches the space of capacity expansions, each of which has a resident-optimal stable assignment that the deferred acceptance method finds. Constructing a good search tree representation significantly boosts the performance of the proposed method. Our simulation shows that the proposed method identifies an almost optimal capacity expansion with a significantly smaller computational budget than exact methods based on mixed-integer programming.