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Combinatorial optimization problems are encountered in many practical contexts such as logistics and production, but exact solutions are particularly difficult to find and usually NP-hard for considerable problem sizes. To compute…

The canonical solution methodology for finite constrained Markov decision processes (CMDPs), where the objective is to maximize the expected infinite-horizon discounted rewards subject to the expected infinite-horizon discounted costs…

Markov decision processes (MDPs) are used to model a wide variety of applications ranging from game playing over robotics to finance. Their optimal policy typically maximizes the expected sum of rewards given at each step of the decision…

Practical reinforcement learning problems are often formulated as constrained Markov decision process (CMDP) problems, in which the agent has to maximize the expected return while satisfying a set of prescribed safety constraints. In this…

Constrained Markov decision processes (CMDPs), in which the agent optimizes expected payoffs while keeping the expected cost below a given threshold, are the leading framework for safe sequential decision making under stochastic…

This paper introduces the Constrained Monte Carlo Tree Search (CMCTS) framework to enhance the mathematical reasoning capabilities of Large Language Models (LLM). By incorporating a constrained action space, Process Reward Model (PRM), and…

Standard planners for sequential decision making (including Monte Carlo planning, tree search, dynamic programming, etc.) are constrained by an implicit sequential planning assumption: The order in which a plan is constructed is the same in…

Monte-Carlo tree search (MCTS) is an effective anytime algorithm with a vast amount of applications. It strategically allocates computational resources to focus on promising segments of the search tree, making it a very attractive search…

Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…

Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring…

Monte Carlo Tree Search (MCTS) has emerged as a powerful tool for decision-making in robotics, enabling efficient exploration of large search spaces. However, traditional MCTS methods struggle in environments characterized by high…

Few real-world hybrid systems are amenable to formal verification, due to their complexity and black box components. Optimization-based falsification---a methodology of search-based testing that employs stochastic optimization---is…

We consider the dynamic classifier selection (DCS) problem: Given an ensemble of classifiers, we are to choose which classifier to use depending on the particular input vector that we get to classify. The problem is a special case of the…

Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (minimize…

A variety of cooperative multi-agent control problems require agents to achieve individual goals while contributing to collective success. This multi-goal multi-agent setting poses difficulties for recent algorithms, which primarily target…

Monte Carlo tree search (MCTS) is one of the most capable online search algorithms for sequential planning tasks, with significant applications in areas such as resource allocation and transit planning. Despite its strong performance in…

Decentralized partially observable Markov decision processes (Dec-POMDPs) are rich models for cooperative decision-making under uncertainty, but are often intractable to solve optimally (NEXP-complete). The transition and observation…

Conflict-Based Search (CBS) is a widely used algorithm for solving multi-agent pathfinding (MAPF) problems optimally. The core idea of CBS is to run hierarchical search, when, on the high level the tree of solutions candidates is explored,…

Monte Carlo Tree Search (MCTS) is a branch of stochastic modeling that utilizes decision trees for optimization, mostly applied to artificial intelligence (AI) game players. This project imagines a game in which an AI player searches for a…

Selecting high-quality candidates from large-scale datasets is critically important in resource-constrained applications such as drug discovery, precision medicine, and the alignment of large language models. While conformal selection…