Monte Carlo Graph Coloring

Graph Coloring is probably one of the most studied and famous problem in graph algorithms. Exact methods fail to solve instances with more than few hundred vertices, therefore, a large number of heuristics have been proposed. Nested Monte Carlo Search (NMCS) and Nested Rollout Policy Adaptation (NRPA) are Monte Carlo search algorithms for single player games. Surprisingly, few work has been dedicated to evaluating Monte Carlo search algorithms to combinatorial graph problems. In this paper we expose how to efficiently apply Monte Carlo search to Graph Coloring and compare this approach to existing ones.

Enhancing Reinforcement Learning Through Guided Search

With the aim of improving performance in Markov Decision Problem in an Off-Policy setting, we suggest taking inspiration from what is done in Offline Reinforcement Learning (RL). In Offline RL, it is a common practice during policy learning to maintain proximity to a reference policy to mitigate uncertainty, reduce potential policy errors, and help improve performance. We find ourselves in a different setting, yet it raises questions about whether a similar concept can be applied to enhance performance ie, whether it is possible to find a guiding policy capable of contributing to performance improvement, and how to incorporate it into our RL agent. Our attention is particularly focused on algorithms based on Monte Carlo Tree Search (MCTS) as a guide.MCTS renowned for its state-of-the-art capabilities across various domains, catches our interest due to its ability to converge to equilibrium in single-player and two-player contexts. By harnessing the power of MCTS as a guide for our RL agent, we observed a significant performance improvement, surpassing the outcomes achieved by utilizing each method in isolation. Our experiments were carried out on the Atari 100k benchmark.

LLMs can Schedule

The job shop scheduling problem (JSSP) remains a significant hurdle in optimizing production processes. This challenge involves efficiently allocating jobs to a limited number of machines while minimizing factors like total processing time or job delays. While recent advancements in artificial intelligence have yielded promising solutions, such as reinforcement learning and graph neural networks, this paper explores the potential of Large Language Models (LLMs) for JSSP. We introduce the very first supervised 120k dataset specifically designed to train LLMs for JSSP. Surprisingly, our findings demonstrate that LLM-based scheduling can achieve performance comparable to other neural approaches. Furthermore, we propose a sampling method that enhances the effectiveness of LLMs in tackling JSSP.

Perfect Information Monte Carlo with Postponing Reasoning

Imperfect information games, such as Bridge and Skat, present challenges due to state-space explosion and hidden information, posing formidable obstacles for search algorithms. Determinization-based algorithms offer a resolution by sampling hidden information and solving the game in a perfect information setting, facilitating rapid and effective action estimation. However, transitioning to perfect information introduces challenges, notably one called strategy fusion.This research introduces `Extended Perfect Information Monte Carlo' (EPIMC), an online algorithm inspired by the state-of-the-art determinization-based approach Perfect Information Monte Carlo (PIMC). EPIMC enhances the capabilities of PIMC by postponing the perfect information resolution, reducing alleviating issues related to strategy fusion. However, the decision to postpone the leaf evaluator introduces novel considerations, such as the interplay between prior levels of reasoning and the newly deferred resolution. In our empirical analysis, we investigate the performance of EPIMC across a range of games, with a particular focus on those characterized by varying degrees of strategy fusion. Our results demonstrate notable performance enhancements, particularly in games where strategy fusion significantly impacts gameplay. Furthermore, our research contributes to the theoretical foundation of determinization-based algorithms addressing challenges associated with strategy fusion.%, thereby enhancing our understanding of these algorithms within the context of imperfect information game scenarios.

Deep Reinforcement Learning for 5*5 Multiplayer Go

In recent years, much progress has been made in computer Go and most of the results have been obtained thanks to search algorithms (Monte Carlo Tree Search) and Deep Reinforcement Learning (DRL). In this paper, we propose to use and analyze the latest algorithms that use search and DRL (AlphaZero and Descent algorithms) to automatically learn to play an extended version of the game of Go with more than two players. We show that using search and DRL we were able to improve the level of play, even though there are more than two players.

Mixture of Public and Private Distributions in Imperfect Information Games

In imperfect information games (e.g. Bridge, Skat, Poker), one of the fundamental considerations is to infer the missing information while at the same time avoiding the disclosure of private information. Disregarding the issue of protecting private information can lead to a highly exploitable performance. Yet, excessive attention to it leads to hesitations that are no longer consistent with our private information. In our work, we show that to improve performance, one must choose whether to use a player's private information. We extend our work by proposing a new belief distribution depending on the amount of private and public information desired. We empirically demonstrate an increase in performance and, with the aim of further improving performance, the new distribution should be used according to the position in the game. Our experiments have been done on multiple benchmarks and in multiple determinization-based algorithms (PIMC and IS-MCTS).

Monte Carlo Search Algorithms Discovering Monte Carlo Tree Search Exploration Terms

Monte Carlo Tree Search and Monte Carlo Search have good results for many combinatorial problems. In this paper we propose to use Monte Carlo Search to design mathematical expressions that are used as exploration terms for Monte Carlo Tree Search algorithms. The optimized Monte Carlo Tree Search algorithms are PUCT and SHUSS. We automatically design the PUCT and the SHUSS root exploration terms. For small search budgets of 32 evaluations the discovered root exploration terms make both algorithms competitive with usual PUCT.

Learning a Prior for Monte Carlo Search by Replaying Solutions to Combinatorial Problems

Monte Carlo Search gives excellent results in multiple difficult combinatorial problems. Using a prior to perform non uniform playouts during the search improves a lot the results compared to uniform playouts. Handmade heuristics tailored to the combinatorial problem are often used as priors. We propose a method to automatically compute a prior. It uses statistics on solved problems. It is a simple and general method that incurs no computational cost at playout time and that brings large performance gains. The method is applied to three difficult combinatorial problems: Latin Square Completion, Kakuro, and Inverse RNA Folding.

Generalized Nested Rollout Policy Adaptation with Limited Repetitions

Generalized Nested Rollout Policy Adaptation (GNRPA) is a Monte Carlo search algorithm for optimizing a sequence of choices. We propose to improve on GNRPA by avoiding too deterministic policies that find again and again the same sequence of choices. We do so by limiting the number of repetitions of the best sequence found at a given level. Experiments show that it improves the algorithm for three different combinatorial problems: Inverse RNA Folding, the Traveling Salesman Problem with Time Windows and the Weak Schur problem.

Vision Transformers for Computer Go

Motivated by the success of transformers in various fields, such as language understanding and image analysis, this investigation explores their application in the context of the game of Go. In particular, our study focuses on the analysis of the Transformer in Vision. Through a detailed analysis of numerous points such as prediction accuracy, win rates, memory, speed, size, or even learning rate, we have been able to highlight the substantial role that transformers can play in the game of Go. This study was carried out by comparing them to the usual Residual Networks.