Distributionally Robust Optimization via Ball Oracle Acceleration

• URL: http://arxiv.org/abs/2203.13225v1
• Date: Thu, 24 Mar 2022 17:31:43 GMT
• Title: Distributionally Robust Optimization via Ball Oracle Acceleration
• Abstract summary: We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. Compared to existing algorithms for this problem, we improve complexity by a factor of up to $epsilon-4/3$.
• Score: 8.417186276756336
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that queries a ball optimization oracle, i.e., a subroutine that minimizes the objective within a small ball around the query point. Our main contribution is efficient implementations of this oracle for DRO objectives. For DRO with $N$ non-smooth loss functions, the resulting algorithms find an $\epsilon$-accurate solution with $\widetilde{O}\left(N\epsilon^{-2/3} + \epsilon^{-2}\right)$ first-order oracle queries to individual loss functions. Compared to existing algorithms for this problem, we improve complexity by a factor of up to $\epsilon^{-4/3}$.

Related papers

• Stronger Memory-Query Tradeoffs for Convex Optimization: The Limitations of Subquadratic Memory [65.64123585249297]
  We prove two lower bounds for the first order complexity of minimizing a $d$-dimensional $1$-Lipschitz convex function over the unit ball with $m$ bits of memory.<n>We first show that any such (possibly randomized) algorithm must make $tilde(fracd2sqrtm)$ oracle queries.<n>For deterministic optimization algorithms, we show that $tilde(mind1.6,fracd8/3m2/3)$ queries are required.
  arXiv  Detail & Related papers  (2026-07-21T00:40:59Z)
• Quantum Algorithms for Non-smooth Non-convex Optimization [30.576546266390714]
  This paper considers the problem for finding the $(,epsilon)$-Goldstein stationary point of Lipschitz continuous objective. We construct a zeroth-order quantum estimator for the surrogate oracle function.
  arXiv  Detail & Related papers  (2024-10-21T16:52:26Z)
• Obtaining Lower Query Complexities through Lightweight Zeroth-Order Proximal Gradient Algorithms [65.42376001308064]
  We propose two variance reduced ZO estimators for complex gradient problems. We improve the state-of-the-art function complexities from $mathcalOleft(minfracdn1/2epsilon2, fracdepsilon3right)$ to $tildecalOleft(fracdepsilon2right)$.
  arXiv  Detail & Related papers  (2024-10-03T15:04:01Z)
• The Computational Complexity of Finding Stationary Points in Non-Convex Optimization [53.86485757442486]
  Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-order but smooth objective functions is a computational problem. We show that finding approximate KKT points in constrained optimization is reducible to finding approximate stationary points in unconstrained optimization but the converse is impossible.
  arXiv  Detail & Related papers  (2023-10-13T14:52:46Z)
• An Algorithm with Optimal Dimension-Dependence for Zero-Order Nonsmooth Nonconvex Stochastic Optimization [37.300102993926046]
  We study the complexity of producing neither smooth nor convex points of Lipschitz objectives which are possibly using only zero-order evaluations. Our analysis is based on a simple yet powerful. Goldstein-subdifferential set, which allows recent advancements in. nonsmooth non optimization.
  arXiv  Detail & Related papers  (2023-07-10T11:56:04Z)
• An Oblivious Stochastic Composite Optimization Algorithm for Eigenvalue Optimization Problems [76.2042837251496]
  We introduce two oblivious mirror descent algorithms based on a complementary composite setting. Remarkably, both algorithms work without prior knowledge of the Lipschitz constant or smoothness of the objective function. We show how to extend our framework to scale and demonstrate the efficiency and robustness of our methods on large scale semidefinite programs.
  arXiv  Detail & Related papers  (2023-06-30T08:34:29Z)
• A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization [10.762749887051546]
  We propose two-time scale algorithms: ProxDAS-A and Proxcal$DASA-GT. Unlike prior work, our algorithms achieve comparable complexity without requiring large batch sizes, more complex per-it operations, or stronger assumptions.
  arXiv  Detail & Related papers  (2023-02-20T05:16:18Z)
• Deterministic Nonsmooth Nonconvex Optimization [94.01526844386977]
  We show that randomization is necessary to obtain a dimension-free dimension-free algorithm. Our algorithm yields the first deterministic dimension-free algorithm for optimizing ReLU networks.
  arXiv  Detail & Related papers  (2023-02-16T13:57:19Z)
• Quadratic Memory is Necessary for Optimal Query Complexity in Convex Optimization: Center-of-Mass is Pareto-Optimal [23.94542304111204]
  We show that quadratic memory is necessary to achieve the optimal oracle complexity for first-order convex optimization. We prove that to minimize $1$-Lipschitz convex functions over the unit ball to $1/d4$ accuracy, any deterministic first-order algorithms using at most $d2-delta$ bits of memory must make $tildeOmega(d1+delta/3)$ queries.
  arXiv  Detail & Related papers  (2023-02-09T22:37:27Z)
• ReSQueing Parallel and Private Stochastic Convex Optimization [59.53297063174519]
  We introduce a new tool for BFG convex optimization (SCO): a Reweighted Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. We develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings.
  arXiv  Detail & Related papers  (2023-01-01T18:51:29Z)
• The First Optimal Acceleration of High-Order Methods in Smooth Convex Optimization [88.91190483500932]
  We study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. The reason for this is that these algorithms require performing a complex binary procedure, which makes them neither optimal nor practical. We fix this fundamental issue by providing the first algorithm with $mathcalOleft(epsilon-2/(p+1)right) $pth order oracle complexity.
  arXiv  Detail & Related papers  (2022-05-19T16:04:40Z)
• Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction [18.65143269806133]
  We consider Proximal Incremental First-order (PIFO) algorithms which have access to gradient and proximal oracle for each individual component. We develop a novel approach for constructing adversarial problems, which partitions the tridiagonal matrix of classical examples into $n$ groups.
  arXiv  Detail & Related papers  (2021-03-15T11:20:31Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• FANOK: Knockoffs in Linear Time [73.5154025911318]
  We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems. We test our methods on problems with $p$ as large as $500,000$.
  arXiv  Detail & Related papers  (2020-06-15T21:55:34Z)

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.