Optimization and Risk Management in Machine Learning

The field of machine learning is moving towards developing more robust and efficient optimization algorithms, with a focus on handling nonconvex and risk-sensitive problems. Recent advances have led to the development of parameter-free optimal rates for nonlinear semi-norm contractions, which have applications in Q-learning and TD-learning. Additionally, there is a growing interest in analyzing and controlling tail risk in various optimization problems, including ski rental and reinforcement learning. Noteworthy papers in this area include: Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to Q-Learning, which achieves parameter-free optimal convergence rates for Q-learning. Policy Newton methods for Distortion Riskmetrics, which proposes a cubic-regularized policy Newton algorithm for solving risk-sensitive control problems in reinforcement learning. Online Convex Optimization with Heavy Tails, which examines old algorithms for online convex optimization in the heavy-tailed setting and establishes new regret bounds without any algorithmic modification.

Sources

Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to $Q$-Learning

Analysis of Schedule-Free Nonconvex Optimization

Controlling tail risk in two-slope ski rental

Policy Newton methods for Distortion Riskmetrics

Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications

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