(Bandit) Convex Optimization with Biased Noisy Gradient Oracles

Abstract

Algorithms for bandit convex optimization and online learning often rely on constructing noisy gradient estimates, which are then used in appropriately adjusted first-order algorithms, replacing actual gradients. Depending on the properties of the function to be optimized and the nature of ``noise'' in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle. With the help of the new framework we unify previous works, reproducing their results in a clean and concise fashion, while, perhaps more importantly, the framework also allows us to formally show that to achieve the optimal root-$n$ rate either the algorithms that use existing gradient estimators, or the proof techniques used to analyze them have to go beyond what exists today.

References in corpus (4)

• On Zeroth-Order Stochastic Convex Optimization via Random Walks
• Multi-scale exploration of convex functions and bandit convex optimization
• Stochastic Intermediate Gradient Method for Convex Problems with Inexact Stochastic Oracle
• Exploiting Smoothness in Statistical Learning, Sequential Prediction, and Stochastic Optimization

Cited by in corpus (2)

• An Accelerated Directional Derivative Method for Smooth Stochastic Convex Optimization
• Minimax Optimal Online Stochastic Learning for Sequences of Convex Functions under Sub-Gradient Observation Failures