Data-driven first-order methods for misspecified convex optimization problems: Global convergence and Rate estimates

Hesam Ahmadi, Uday V. Shanbhag

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations

Abstract

We consider a misspecified optimization problem that requires minimizing of a convex function f(x; θ) in x over a closed and convex set X where θ∗ is an unknown vector of parameters. Suppose θ∗ may be learnt by a parallel learning process that generates a sequence of estimators θk, each of which is an increasingly accurate approximation of θ. In this context, we examine the development of coupled schemes that generate iterates (xk, θk) such that as the iteration index k → ∞, then xk → x, a minimizer of f(x; θ) over X and θk → θ.We make two sets of contributions along this direction. First, we consider the use of gradient methods and proceed to show that such techniques are globally convergent. In addition, such schemes show a quantifiable degradation in the linear rate of convergence observed for strongly convex optimization problems. When strong convexity assumptions are weakened, we see a modification in the convergence rate in function values of O(1/K) by an additive factor θ0-θO(qKg +1/K) where θ0-θ represents the initial misspecification in θ∗ and qg denotes the contractive factor associated with the learning process. Second, we present an averaging-based subgradient scheme and show that the optimal constant steplength leads to a modification in the rate by θ0-θO(qKg +1/K), implying no effect on the standard rate of O(1/√K).

Original languageEnglish (US)
Article number7040048
Pages (from-to)4228-4233
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Fingerprint

Dive into the research topics of 'Data-driven first-order methods for misspecified convex optimization problems: Global convergence and Rate estimates'. Together they form a unique fingerprint.

Cite this