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Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for…

We give polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs). Specifically, given a BMDP, and given an initial population, where the objective of the controller…

Stochastic two-player games model systems with an environment that is both adversarial and stochastic. The adversarial part of the environment is modeled by a player (Player 2) who tries to prevent the system (Player 1) from achieving its…

Value iteration (VI) is a foundational dynamic programming method, important for learning and planning in optimal control and reinforcement learning. VI proceeds in batches, where the update to the value of each state must be completed…

Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.),…

Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the…

Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of…

We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this…

Partially Observable Markov Decision Processes (POMDPs) are fundamental to decision-making under uncertainty. We introduce a novel scalable approach to accelerate upper bound estimation in Point-Based Value Iteration (PBVI) algorithms, the…

We study two-player concurrent stochastic games on finite graphs, with B\"uchi and co-B\"uchi objectives. The goal of the first player is to maximize the probability of satisfying the given objective. Following Martin's determinacy theorem…

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal,…

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…

The maximal biclique enumeration problem in bipartite graphs is fundamental and has numerous applications in E-commerce and transaction networks. Most existing studies adopt a branch-and-bound framework, which recursively expands a partial…

We study 2-player zero-sum concurrent (i.e., simultaneous move) stochastic B\"uchi games and Transience games on countable graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of satisfying the game…

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

We consider the classic budgeted maximum weight independent set (BMWIS) problem. The input is a graph $G = (V,E)$, a weight function $w:V \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:V \rightarrow \mathbb{R}_{\geq 0}$, and a budget…

An algorithm is proposed to verify whether a finite game is a weighted potential game (WPG) without pre-knowledge on its weights. Then the algorithm is also applied to find the closest WPG for a given finite game. The concept and criterion…

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…

Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…