• Problem Setup • Multi-Armed Bandits • Bandit Convex Optimization • Advanced Topics

• Two-player Zero-sum Games • Minimax Theorem • Repeated Play • Faster Convergence via Adaptivity

• Optimistic Online Mirror Descent • A Unified Framework • Small-Loss bound • Gradient-Variance bound • Gradient-Variation bound

• Motivation • Small-Loss Bounds • Small-Loss bound for PEA • Self-confident Tuning • Small-Loss bound for OCO

• Algorithmic Framework • Regret Analysis • Interpretation from Primal-Dual View • Follow-the-Regularized Leader

• Problem Setup • Algorithms • Connection to Online Convex Optimization

• Online Learning • Online Convex Optimization • Convex Functions • Strongly Convex Functions • Exp-concave Functions

• GD for Smooth Optimization • Smooth and Convex Functions • Smooth and Strongly Convex Functions • Nesterov’s Accelerated GD • Extension to Composite Optimization

• Gradient Descent • Convex and Lipschitz • Polyak Step Size • Convergence without Optimal Value • Optimal Time-Varying Step Sizes • Strongly Convex and Lipschitz

• Convex Set and Convex Function • Convex Optimization Problem • Optimality Condition • Function Properties