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.

Related papers

• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity [59.75300530380427]
  We consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.
  arXiv  Detail & Related papers  (2024-06-28T02:56:22Z)
• Stochastic Nested Compositional Bi-level Optimization for Robust Feature Learning [11.236838268731804]
  We develop and analyze algorithms for solving nested bi-level optimization problems. Our proposed algorithm does not rely on matrix complexity or mini-batches.
  arXiv  Detail & Related papers  (2023-07-11T15:52:04Z)
• Optimizing NOTEARS Objectives via Topological Swaps [41.18829644248979]
  In this paper, we develop an effective method for a set of candidate algorithms. At the inner level, given a subject, we utilize off-the-the-art constraints. The proposed method significantly improves the score of other algorithms.
  arXiv  Detail & Related papers  (2023-05-26T21:49:37Z)
• Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization [88.0031283949404]
  Many real-world problems have complicated non functional constraints and use a large number of data points. Our proposed method outperforms an existing method with the previously best-known result.
  arXiv  Detail & Related papers  (2022-12-19T14:48:54Z)
• Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization [94.19177623349947]
  Non-smooth non optimization problems emerge in machine learning and business making. Two core challenges impede the development of efficient methods with finitetime convergence guarantee. Two-phase versions of GFM and SGFM are also proposed and proven to achieve improved large-deviation results.
  arXiv  Detail & Related papers  (2022-09-12T06:53:24Z)
• Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming [5.126924253766052]
  We show that the proposed method exhibits a linear convergence rate for solving sharp instances with a high probability. We also propose an efficient coordinate-based oracle for unconstrained bilinear problems.
  arXiv  Detail & Related papers  (2021-11-10T04:56:38Z)
• Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming [17.9230793188835]
  We study nonlinear optimization problems with objective and deterministic equality and inequality constraints. We propose an active-set sequentialAdaptive programming algorithm, using a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the parameters of augmented Lagrangian and performs line search to decide the stepsize.
  arXiv  Detail & Related papers  (2021-09-23T17:12:17Z)
• Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization [12.742028139557384]
  We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for solving convex-concave min-max problems with finite sum structure. We prove that the algorithm enjoys the same convergence rate as that of zeroth-order algorithms for convex minimization problems.
  arXiv  Detail & Related papers  (2021-06-16T18:49:59Z)
• Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms [69.45237691598774]
  We study the problem of least squares linear regression where the data-points are dependent and are sampled from a Markov chain. We establish sharp information theoretic minimax lower bounds for this problem in terms of $tau_mathsfmix$. We propose an algorithm based on experience replay--a popular reinforcement learning technique--that achieves a significantly better error rate.
  arXiv  Detail & Related papers  (2020-06-16T04:26:50Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.