English
Related papers

Related papers: Universal Complexity Bounds Based on Value Iterati…

200 papers

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

Formal Languages and Automata Theory · Computer Science 2023-06-22 Thomas Colcombet , Nathanaël Fijalkow , Paweł Gawrychowski , Pierre Ohlmann

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…

Combinatorics · Mathematics 2015-07-31 Xavier Allamigeon , Pascal Benchimol , Stéphane Gaubert , Michael Joswig

The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the cost incurred between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games…

Logic in Computer Science · Computer Science 2023-06-22 Alexander Weinert , Martin Zimmermann

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a…

Computer Science and Game Theory · Computer Science 2019-05-31 Alberto Marchesi , Matteo Castiglioni , Nicola Gatti

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

Computer Science and Game Theory · Computer Science 2021-04-30 Markus Brill , Rupert Freeman , Vincent Conitzer

We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…

Computer Science and Game Theory · Computer Science 2022-07-21 Krishnendu Chatterjee , Joost-Pieter Katoen , Maximilian Weininger , Tobias Winkler

Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…

Computational Complexity · Computer Science 2018-06-26 Pravesh K. Kothari , Ruta Mehta

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

Computer Science and Game Theory · Computer Science 2018-09-12 Alexander Weinert

This paper aims to establish an entropy-regularized value-based reinforcement learning method that can ensure the monotonic improvement of policies at each policy update. Unlike previously proposed lower-bounds on policy improvement in…

Machine Learning · Computer Science 2020-08-26 Lingwei Zhu , Takamitsu Matsubara

In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…

Information Theory · Computer Science 2016-03-08 Mrinalkanti Ghosh , Satyadev Nandakumar

We introduce a contractive abstract dynamic programming framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure. Aside from greater generality, the…

Computer Science and Game Theory · Computer Science 2021-10-22 Dimitri Bertsekas

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a…

Computer Science and Game Theory · Computer Science 2014-09-12 Xavier Allamigeon , Pascal Benchimol , Stéphane Gaubert

We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence…

Probability · Mathematics 2018-01-25 Sylvain Delattre , Nicolas Fournier

A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…

Optimization and Control · Mathematics 2017-01-31 Andreas H. Hamel , Andreas Loehne

We study countably infinite Markov decision processes (MDPs) with real-valued transition rewards. Every infinite run induces the following sequences of payoffs: 1. Point payoff (the sequence of directly seen transition rewards), 2. Total…

Artificial Intelligence · Computer Science 2021-07-13 Richard Mayr , Eric Munday

The analysis of equilibrium points in random games has been of great interest in evolutionary game theory, with important implications for understanding of complexity in a dynamical system, such as its behavioural, cultural or biological…

Analysis of PDEs · Mathematics 2018-07-09 Manh Hong Duong , Hoang Minh Tran , The Anh Han

The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite multiple insightful results in the past few years, a proof for…

Dynamical Systems · Mathematics 2024-04-25 Tuhin Sahai , Abeynaya Gnanasekaran

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Machine Learning · Computer Science 2024-09-06 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman

Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive…

Computer Science and Game Theory · Computer Science 2023-01-12 Xiaotie Deng , Ningyuan Li , David Mguni , Jun Wang , Yaodong Yang

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…

Logic in Computer Science · Computer Science 2026-04-30 Marnix Suilen , Guillermo A. Pérez