Constrained Stochastic Nonconvex Optimization with State-dependent Markov DataDownload PDF

Published: 31 Oct 2022, Last Modified: 15 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: Constrained Optimization, Nonconvex Optimization, Projection-free Algorithm, Dependent Data, State-dependent Markov Data
TL;DR: We provide a projection-free stochastic algorithm for nonconvex optimization with state-dependent Markov data with applications to strategic classification and reinforcement learning.
Abstract: We study stochastic optimization algorithms for constrained nonconvex stochastic optimization problems with Markovian data. In particular, we focus on the case when the transition kernel of the Markov chain is state-dependent. Such stochastic optimization problems arise in various machine learning problems including strategic classification and reinforcement learning. For this problem, we study both projection-based and projection-free algorithms. In both cases, we establish that the number of calls to the stochastic first-order oracle to obtain an appropriately defined $\epsilon$-stationary point is of the order $\mathcal{O}(1/\epsilon^{2.5})$. In the projection-free setting we additionally establish that the number of calls to the linear minimization oracle is of order $\mathcal{O}(1/\epsilon^{5.5})$. We also empirically demonstrate the performance of our algorithm on the problem of strategic classification with neural networks.
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