Related papers: ZERO: Playing Mathematical Programming Games
Max-min bilinear optimization models, where one agent maximizes and an adversary minimizes a common bilinear objective, serve as canonical saddle-point formulations in optimization theory. They capture, among others, two-player zero-sum…
The game of Go has long served as a benchmark for artificial intelligence, demanding sophisticated strategic reasoning and long-term planning. Previous approaches such as AlphaGo and its successors, have predominantly relied on model-based…
Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
Robust optimization is a very popular means to address decision-making problems affected by uncertainty. Its success has been fueled by its attractive robustness and scalability properties, by ease of modeling, and by the limited…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving…
This paper considers two-player zero-sum finite-horizon Markov games with simultaneous moves. The study focuses on the challenging settings where the value function or the model is parameterized by general function classes. Provably…
The balancing process for game levels in a competitive two-player context involves a lot of manual work and testing, particularly in non-symmetrical game levels. In this paper, we propose an architecture for automated balancing of…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Assistance games are a promising alternative to reinforcement learning from human feedback (RLHF) for training AI assistants. Assistance games resolve key drawbacks of RLHF, such as incentives for deceptive behavior, by explicitly modeling…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental…
Task scheduling is an important and complex problem in computational grid. A computational grid often covers a range of different kinds of nodes, which offers a complex environment. There is a need to develop algorithms that can capture…
Zero-sum Markov Stackelberg games can be used to model myriad problems, in domains ranging from economics to human robot interaction. In this paper, we develop policy gradient methods that solve these games in continuous state and action…
Integer programming games (IPGs) are n-person games with integer strategy spaces. These games are used to model non-cooperative combinatorial decision-making and are used in domains such as cybersecurity and transportation. The prevalent…
In this paper, we consider a class of $n$-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix…
Reinforcement learning (RL) has been widely applied to game-playing and surpassed the best human-level performance in many domains, yet there are few use-cases in industrial or commercial settings. We introduce OR-Gym, an open-source…
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…