Projection-free Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data

• URL: http://arxiv.org/abs/2206.11346v1
• Date: Wed, 22 Jun 2022 19:43:15 GMT
• Title: Projection-free Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data
• Authors: Abhishek Roy (1), Krishnakumar Balasubramanian (1), Saeed Ghadimi (2) ((1) Department of Statistics, University of California, Davis, (2) Department of Management Sciences, University of Waterloo)
• Abstract summary: We show a projection-free gradient-type algorithm for constrained non- Markovian case chain problems with Markovian data. We also empirically demonstrate the performance of our algorithm on the problem of strategic classification with neural networks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a projection-free conditional gradient-type algorithm 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 establish that the number of calls to the stochastic first-order oracle and the linear minimization oracle to obtain an appropriately defined $\epsilon$-stationary point, are of the order $\mathcal{O}(1/\epsilon^{2.5})$ and $\mathcal{O}(1/\epsilon^{5.5})$ respectively. We also empirically demonstrate the performance of our algorithm on the problem of strategic classification with neural networks.

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