Related papers: On the optimal pivot path of simplex method for li…

Standard approaches for global optimization of non-convex functions, such as branch-and-bound, maintain partition trees to systematically prune the domain. The tree size grows exponentially in the number of dimensions. We propose new…

Polly is the LLVM project's polyhedral loop nest optimizer. Recently, user-directed loop transformation pragmas were proposed based on LLVM/Clang and Polly. The search space exposed by the transformation pragmas is a tree, wherein each node…

Making changes to a program to optimize its performance is an unscalable task that relies entirely upon human intuition and experience. In addition, companies operating at large scale are at a stage where no single individual understands…

Monte Carlo Tree Search (MCTS) is a powerful algorithm for solving complex decision-making problems. This paper presents an optimized MCTS implementation applied to the FrozenLake environment, a classic reinforcement learning task…

Large language models (LLMs) have demonstrated remarkable capabilities in code generation and structured reasoning; however, their performance often degrades on complex tasks that require consistent multi-step planning. Recent work has…

Model-based reinforcement learning (RL) methods that leverage search are responsible for many milestone breakthroughs in RL. Sequential Monte Carlo (SMC) recently emerged as an alternative to the Monte Carlo Tree Search (MCTS) algorithm…

A novel method called mixed variable system Monte Carlo tree search (MVSMCTS) formulation is presented for optimization problems considering various types of variables with single and mixed continuous-discrete system. This method utilizes a…

Gradient-based methods are often used for policy optimization in deep reinforcement learning, despite being vulnerable to local optima and saddle points. Although gradient-free methods (e.g., genetic algorithms or evolution strategies) help…

It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…

Online motion planning is a challenging problem for intelligent robots moving in dense environments with dynamic obstacles, e.g., crowds. In this work, we propose a novel approach for optimal and safe online motion planning with minimal…

Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms in order to solve large scale…

Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a "small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching…

In many environmental monitoring scenarios, the sampling robot needs to simultaneously explore the environment and exploit features of interest with limited time. We present an anytime multi-objective informative planning method called…

Optimal motion planning involves obstacles avoidance where path planning is the key to success in optimal motion planning. Due to the computational demands, most of the path planning algorithms can not be employed for real-time based…

While chain-of-thought prompting with Best-of-N (BoN) selection has become popular for mathematical reasoning in large language models (LLMs), its linear structure fails to capture the branching and exploratory nature of complex…

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…

We explore applying the Monte Carlo Tree Search (MCTS) algorithm in a notoriously difficult task: tuning programs for high-performance deep learning and image processing. We build our framework on top of Halide and show that MCTS can…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…