Related papers: Sample-and-Bound for Non-Convex Optimization

Monte Carlo Tree Search (MCTS) algorithms have achieved great success on many challenging benchmarks (e.g., Computer Go). However, they generally require a large number of rollouts, making their applications costly. Furthermore, it is also…

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

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…

We explore how a general AI algorithm can be used for 3D scene understanding to reduce the need for training data. More exactly, we propose a modification of the Monte Carlo Tree Search (MCTS) algorithm to retrieve objects and room layouts…

Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo…

Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…

Monte-Carlo Tree Search (MCTS) is a family of sampling-based search algorithms widely used for online planning in sequential decision-making domains and at the heart of many recent advances in artificial intelligence. Understanding the…

We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates…

Tree search-based methods have made significant progress in enhancing the code generation capabilities of large language models. However, due to the difficulty in effectively evaluating intermediate algorithmic steps and the inability to…

This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

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…

While plan-and-infill decoding in Masked Diffusion Models (MDMs) shows promise for mathematical and code reasoning, performance remains highly sensitive to slot infilling order, often yielding substantial output variance. We introduce…

Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain…

In this paper we explore the application of simultaneous move Monte Carlo Tree Search (MCTS) based online framework for tactical maneuvering between two unmanned aircrafts. Compared to other techniques, MCTS enables efficient search over…

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…

In this paper, we consider the online computation of a strategy that aims at optimizing the expected average reward in a Markov decision process. The strategy is computed with a receding horizon and using Monte Carlo tree search (MCTS). We…

The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…

In many applications of computer algebra large expressions must be simplified to make repeated numerical evaluations tractable. Previous works presented heuristically guided improvements, e.g., for Horner schemes. The remaining expression…