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Consider a scenario where a player chooses an action in each round $t$ out of $T$ rounds and observes the incurred cost after a delay of $d_{t}$ rounds. The cost functions and the delay sequence are chosen by an adversary. We show that in a…

Machine Learning · Computer Science 2022-05-16 Ilai Bistritz , Zhengyuan Zhou , Xi Chen , Nicholas Bambos , Jose Blanchet

In this paper, we tackle the challenging problem of delayed rewards in reinforcement learning (RL). While Proximal Policy Optimization (PPO) has emerged as a leading Policy Gradient method, its performance can degrade under delayed rewards.…

Understanding the behavior of no-regret dynamics in general $N$-player games is a fundamental question in online learning and game theory. A folk result in the field states that, in finite games, the empirical frequency of play under…

Computer Science and Game Theory · Computer Science 2020-10-21 Lampros Flokas , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Thanasis Lianeas , Panayotis Mertikopoulos , Georgios Piliouras

Reinforcement Learning (RL) heavily relies on the careful design of the reward function. However, accurately assigning rewards to each state-action pair in Long-Term Reinforcement Learning (LTRL) tasks remains a significant challenge. As a…

Machine Learning · Computer Science 2025-06-03 Qi Ju , Falin Hei , Zhemei Fang , Yunfeng Luo

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

Computer Science and Game Theory · Computer Science 2021-10-19 Yu-Guan Hsieh , Kimon Antonakopoulos , Panayotis Mertikopoulos

No-regret learning has a long history of being closely connected to game theory. Recent works have devised uncoupled no-regret learning dynamics that, when adopted by all the players in normal-form games, converge to various equilibrium…

Computer Science and Game Theory · Computer Science 2024-04-24 Weichao Mao , Haoran Qiu , Chen Wang , Hubertus Franke , Zbigniew Kalbarczyk , Tamer Başar

Inspired by the demands of real-time climate and weather forecasting, we develop optimistic online learning algorithms that require no parameter tuning and have optimal regret guarantees under delayed feedback. Our algorithms -- DORM,…

We revisit the fundamental problem of prediction with expert advice, in a setting where the environment is benign and generates losses stochastically, but the feedback observed by the learner is subject to a moderate adversarial corruption.…

Machine Learning · Computer Science 2021-07-05 Idan Amir , Idan Attias , Tomer Koren , Roi Livni , Yishay Mansour

In this paper, we investigate how randomness and uncertainty influence learning in games. Specifically, we examine a perturbed variant of the dynamics of "follow-the-regularized-leader" (FTRL), where the players' payoff observations and…

Computer Science and Game Theory · Computer Science 2025-06-17 Pierre-Louis Cauvin , Davide Legacci , Panayotis Mertikopoulos

Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…

Computer Science and Game Theory · Computer Science 2022-03-24 Ioannis Anagnostides , Ioannis Panageas , Gabriele Farina , Tuomas Sandholm

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…

Computer Science and Game Theory · Computer Science 2025-01-22 Yang Cai , Gabriele Farina , Julien Grand-Clément , Christian Kroer , Chung-Wei Lee , Haipeng Luo , Weiqiang Zheng

Online learning with delayed feedback has received increasing attention recently due to its several applications in distributed, web-based learning problems. In this paper we provide a systematic study of the topic, and analyze the effect…

Machine Learning · Computer Science 2015-07-02 Pooria Joulani , András György , Csaba Szepesvári

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ worst-case…

Machine Learning · Computer Science 2020-06-16 Arun Sai Suggala , Praneeth Netrapalli

We investigate a nonstochastic bandit setting in which the loss of an action is not immediately charged to the player, but rather spread over the subsequent rounds in an adversarial way. The instantaneous loss observed by the player at the…

Machine Learning · Computer Science 2022-09-27 Nicolò Cesa-Bianchi , Tommaso Cesari , Roberto Colomboni , Claudio Gentile , Yishay Mansour

In two-player zero-sum games, the learning dynamic based on optimistic Hedge achieves one of the best-known regret upper bounds among strongly-uncoupled learning dynamics. With an appropriately chosen learning rate, the social and…

Machine Learning · Computer Science 2025-10-14 Taira Tsuchiya

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a…

Machine Learning · Computer Science 2022-01-11 Daron Anderson , George Iosifidis , Douglas J. Leith

Reinforcement Learning (RL) in games has gained significant momentum in recent years, enabling the creation of different agent behaviors that can transform a player's gaming experience. However, deploying RL agents in production…

Artificial Intelligence · Computer Science 2025-07-01 António Afonso , Iolanda Leite , Alessandro Sestini , Florian Fuchs , Konrad Tollmar , Linus Gisslén

This paper brings the concept of ``optimism" to the new and promising framework of online Non-stochastic Control (NSC). Namely, we study how NSC can benefit from a prediction oracle of unknown quality responsible for forecasting future…

Machine Learning · Computer Science 2024-08-27 Naram Mhaisen , George Iosifidis

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…

Computer Science and Game Theory · Computer Science 2025-08-05 Wataru Masaka , Mitsuki Sakamoto , Kenshi Abe , Kaito Ariu , Tuomas Sandholm , Atsushi Iwasaki

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…