Stochastic Bandits with ReLU Neural Networks

• URL: http://arxiv.org/abs/2405.07331v1
• Date: Sun, 12 May 2024 16:54:57 GMT
• Title: Stochastic Bandits with ReLU Neural Networks
• Authors: Kan Xu, Hamsa Bastani, Surbhi Goel, Osbert Bastani,
• Abstract summary: We show that a $tildeO(sqrtT)$ regret guarantee is achievable by considering bandits with one-layer ReLU neural networks. We propose an OFU-ReLU algorithm that can achieve this upper bound.
• Score: 40.41457480347015
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the stochastic bandit problem with ReLU neural network structure. We show that a $\tilde{O}(\sqrt{T})$ regret guarantee is achievable by considering bandits with one-layer ReLU neural networks; to the best of our knowledge, our work is the first to achieve such a guarantee. In this specific setting, we propose an OFU-ReLU algorithm that can achieve this upper bound. The algorithm first explores randomly until it reaches a linear regime, and then implements a UCB-type linear bandit algorithm to balance exploration and exploitation. Our key insight is that we can exploit the piecewise linear structure of ReLU activations and convert the problem into a linear bandit in a transformed feature space, once we learn the parameters of ReLU relatively accurately during the exploration stage. To remove dependence on model parameters, we design an OFU-ReLU+ algorithm based on a batching strategy, which can provide the same theoretical guarantee.

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