Sequential identification questions in game trees with stochastic payoffs arise naturally as robust versions of bandit problems.

The Long-Range (LoRa) protocol, known for its extensive range and low power, has increasingly been adopted in tags worn by mentally incapacitated persons (MIPs) and others at risk of going missing. We study the sequential decision-making process for a mobile sensor to locate a periodically broadcasting LoRa tag with the fewest moves (hops) in general, unknown environments, guided by the received signal strength indicator (RSSI). While existing methods leverage reinforcement learning for search, they remain vulnerable to domain shift and signal fluctuation, resulting in cascading decision errors that culminate in substantial localization inaccuracies. To bridge this gap, we propose LoRaCompass, a reinforcement learning model designed to achieve robust and efficient search for a LoRa tag. For exploitation under domain shift and signal fluctuation, LoRaCompass learns a robust spatial representation from RSSI to maximize the probability of moving closer to a tag, via a spatially-aware feature extractor and a policy distillation loss function. It further introduces an exploration function inspired by the upper confidence bound (UCB) that guides the sensor toward the tag with increasing confidence. We have validated LoRaCompass in ground-based and drone-assisted scenarios within diverse unseen environments covering an area of over 80km^2. It has demonstrated high success rate (>90%) in locating the tag within 100m proximity (a 40% improvement over existing methods) and high efficiency with a search path length (in hops) that scales linearly with the initial distance.

Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal is to quickly identify the optimal move in a given game tree by sequentially sampling its stochastic payoffs. We develop new algorithms for trees of arbitrary depth, that operate by summarizing all deeper levels of the tree into confidence intervals at depth one, and applying a best arm identification procedure at the root. We prove new sample complexity guarantees with a refined dependence on the problem instance. We show experimentally that our algorithms outperform existing elimination-based algorithms and match previous special-purpose methods for depth-two trees.

In this memorial paper, we honor Tze Leung Lai's seminal contributions to the topic of multi-armed bandits, with a specific focus on his pioneering work on the upper confidence bound. We establish sharp non-asymptotic regret bounds for an upper confidence bound index with a constant level of exploration for Gaussian rewards. Furthermore, we establish a non-asymptotic regret bound for the upper confidence bound index of Lai (1987) which employs an exploration function that decreases with the sample size of the corresponding arm. The regret bounds have leading constants that match the Lai-Robbins lower bound. Our results highlight an aspect of Lai's seminal works that deserves more attention in the machine learning literature.

Multi-agent reinforcement learning (MARL) is employed to develop autonomous agents that can learn to adopt cooperative or competitive strategies within complex environments. However, the linear increase in the number of agents leads to a combinatorial explosion of the action space, which may result in algorithmic instability, difficulty in convergence, or entrapment in local optima. While researchers have designed a variety of effective algorithms to compress the action space, these methods also introduce new challenges, such as the need for manually designed prior knowledge or reliance on the structure of the problem, which diminishes the applicability of these techniques. In this paper, we introduce Evolutionary action SPAce Reduction with Knowledge (eSpark), an exploration function generation framework driven by large language models (LLMs) to boost exploration and prune unnecessary actions in MARL. Using just a basic prompt that outlines the overall task and setting, eSpark is capable of generating exploration functions in a zero-shot manner, identifying and pruning redundant or irrelevant state-action pairs, and then achieving autonomous improvement from policy feedback. In reinforcement learning tasks involving inventory management and traffic light control encompassing a total of 15 scenarios, eSpark consistently outperforms the combined MARL algorithm in all scenarios, achieving an average performance gain of 34.4% and 9.9% in the two types of tasks respectively. Additionally, eSpark has proven to be capable of managing situations with a large number of agents, securing a 29.7% improvement in scalability challenges that featured over 500 agents. The code can be found in https://github.com/LiuZhihao2022/eSpark.git.

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduces balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.

Optimization problems involving mixed variables, i.e., variables of numerical and categorical nature, can be challenging to solve, especially in the presence of complex constraints. Moreover, when the objective function is the result of a complicated simulation or experiment, it may be expensive to evaluate. This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems up to medium-large size (around 100 variables after encoding and 20 constraints) based on constructing a piecewise affine surrogate of the objective function over feasible samples. We introduce two types of exploration functions to efficiently search the feasible domain via mixed-integer linear programming solvers. We also provide a preference-based version of the algorithm, which can be used when only pairwise comparisons between samples can be acquired while the underlying objective function to minimize remains unquantified. The two algorithms are tested on mixed-variable benchmark problems with and without constraints. The results show that, within a small number of acquisitions, the proposed algorithms can often achieve better or comparable results than other existing methods.

This post assumes that you are familiar with the basics of Reinforcement Learning(RL) and Markov Decision Processes, if not please refer to this previous post first. Let's consider a problem where the agent can be in various states and can choose an action from a set of actions. Such type of problems are called Sequential Decision Problems. The solution to an MDP is an optimal policy which refers to the choice of action for every state that maximizes overall cumulative reward. Thus, the transition model that represents an agent's environment(when the environment is known) and the optimal policy which decides what action the agent needs to perform in each state are required elements for training the agent learn a specific behavior.

Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal is to quickly identify the optimal move in a given game tree by sequentially sampling its stochastic payoffs. We develop new algorithms for trees of arbitrary depth, that operate by summarizing all deeper levels of the tree into confidence intervals at depth one, and applying a best arm identification procedure at the root. We prove new sample complexity guarantees with a refined dependence on the problem instance. We show experimentally that our algorithms outperform existing elimination-based algorithms and match previous special-purpose methods for depth-two trees.

We consider two-player zero-sum turn-based interactions, in which the sequence of possible successive moves is represented by a maximin game tree T. This tree models the possible actions sequences by a collection of MAX nodes, that correspond to states in the game in which player A should take action, MIN nodes, for states in the game in which player B should take action, and leaves which specify the payoff for player A. The goal is to determine the best action at the root for player A. For deterministic payoffs this search problem is primarily algorithmic, with several powerful pruning strategies available [20]. We look at problems with stochastic payoffs, which in addition present a major statistical challenge. Sequential identification questions in game trees with stochastic payoffs arise naturally as robust versions of bandit problems. They are also a core component of Monte Carlo tree search (MCTS) approaches for solving intractably large deterministic tree search problems, where an entire sub-tree is represented by a stochastic leaf in which randomized play-out and/or evaluations are performed [4]. A play-out consists in finishing the game with some simple, typically random, policy and observing the outcome for player A. For example, MCTS is used within the AlphaGo system [21], and the evaluation of a leaf position combines supervised learning and (smart) play-outs. While MCTS algorithms for Go have now reached expert human level, such algorithms remain very costly, in that many (expensive) leaf evaluations or play-outs are necessary to output the next action to be taken by the player. In this paper, we focus on the sample complexity of Monte-Carlo Tree Search methods, about which very little is known. For this purpose, we work under a simplified model for MCTS already studied by [22], and that generalizes the depth-two framework of [10].