Tianpeng Zhang

Haitong Ma, Tianpeng Zhang, Yixuan Wu et al.

We study the multi-agent Bayesian optimization (BO) problem, where multiple agents maximize a black-box function via iterative queries. We focus on Entropy Search (ES), a sample-efficient BO algorithm that selects queries to maximize the mutual information about the maximum of the black-box function. One of the main challenges of ES is that calculating the mutual information requires computationally-costly approximation techniques. For multi-agent BO problems, the computational cost of ES is exponential in the number of agents. To address this challenge, we propose the Gaussian Max-value Entropy Search, a multi-agent BO algorithm with favorable sample and computational efficiency. The key to our idea is to use a normal distribution to approximate the function maximum and calculate its mutual information accordingly. The resulting approximation allows queries to be cast as the solution of a closed-form optimization problem which, in turn, can be solved via a modified gradient ascent algorithm and scaled to a large number of agents. We demonstrate the effectiveness of Gaussian max-value Entropy Search through numerical experiments on standard test functions and real-robot experiments on the source-seeking problem. Results show that the proposed algorithm outperforms the multi-agent BO baselines in the numerical experiments and can stably seek the source with a limited number of noisy observations on real robots.

Tianpeng Zhang, Kasper Johansson, Na Li

The multi-armed bandit(MAB) problem is a simple yet powerful framework that has been extensively studied in the context of decision-making under uncertainty. In many real-world applications, such as robotic applications, selecting an arm corresponds to a physical action that constrains the choices of the next available arms (actions). Motivated by this, we study an extension of MAB called the graph bandit, where an agent travels over a graph to maximize the reward collected from different nodes. The graph defines the agent's freedom in selecting the next available nodes at each step. We assume the graph structure is fully available, but the reward distributions are unknown. Built upon an offline graph-based planning algorithm and the principle of optimism, we design a learning algorithm, G-UCB, that balances long-term exploration-exploitation using the principle of optimism. We show that our proposed algorithm achieves $O(\sqrt{|S|T\log(T)}+D|S|\log T)$ learning regret, where $|S|$ is the number of nodes and $D$ is the diameter of the graph, which matches the theoretical lower bound $Ω(\sqrt{|S|T})$ up to logarithmic factors. To our knowledge, this result is among the first tight regret bounds in non-episodic, un-discounted learning problems with known deterministic transitions. Numerical experiments confirm that our algorithm outperforms several benchmarks.