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2511 results in Pattern Recognition and Machine Learning

Page 9 of 126

  • 1 - Introduction and Problem Statement

  • Tor Lattimore, Google DeepMind, London
  • Book:
    Bandit Convex Optimisation
    Published online:
    07 March 2026
    Print publication:
    19 March 2026, pp 1-13
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  • Summary

    This book is about approximately solving problems of the form.

  • 3 - Mathematical Tools

  • Tor Lattimore, Google DeepMind, London
  • Book:
    Bandit Convex Optimisation
    Published online:
    07 March 2026
    Print publication:
    19 March 2026, pp 26-41

  • Summary

    The purpose of this chapter is to introduce the necessary tools from optimisation, convex geometry and convex analysis. You can safely skip this chapter, referring back as needed. The main concepts introduced are as follows:

  • 8 - Exponential Weights

  • Tor Lattimore, Google DeepMind, London
  • Book:
    Bandit Convex Optimisation
    Published online:
    07 March 2026
    Print publication:
    19 March 2026, pp 94-117

  • Summary

    We already saw an application of exponential weights to linear and quadratic bandits in Chapter 7. The same abstract algorithm can also be used for convex bandits but the situation is more complicated. Throughout this chapter we assume the losses are bounded and there is no noise:

  • 7 - Linear and Quadratic Bandits

  • Tor Lattimore, Google DeepMind, London
  • Book:
    Bandit Convex Optimisation
    Published online:
    07 March 2026
    Print publication:
    19 March 2026, pp 79-93

  • Summary

    Function classes like Fb are non-parametric. In this chapter we shift gears by studying two important parametric classes: Fb,lin and Fb,quad. The main purpose of this chapter is to use the machinery designed for linear bandits to prove an upper bound on the minimax regret for quadratic bandits. On the positive side the approach is both elementary and instructive. More negatively, the resulting algorithm is not computationally efficient. Before the algorithms and regret analysis we need three tools: covering numbers, optimal experimental design and the exponential weights algorithm.

  • 9 - Cutting Plane Methods

  • Tor Lattimore, Google DeepMind, London
  • Book:
    Bandit Convex Optimisation
    Published online:
    07 March 2026
    Print publication:
    19 March 2026, pp 118-144

  • Summary

    Like the bisection method (Chapter 4), cutting plane methods are most naturally suited to the stochastic setting. For the remainder of the chapter we assume the setting is stochastic and the loss function is bounded:

Bandit Convex Optimisation
  • Tor Lattimore
  • Published online:
    07 March 2026
    Print publication:
    19 March 2026
  • This comprehensive reference brings readers to the frontier of research on bandit convex optimization or zeroth-order convex optimization. The focus is on theoretical aspects, with short, self-contained chapters covering all the necessary tools from convex optimization and online learning, including gradient-based algorithms, interior point methods, cutting plane methods and information-theoretic machinery. The book features a large number of exercises, open problems and pointers to future research directions, making it ideal for students as well as researchers.

Introduction to Online Control
  • Elad Hazan, Karan Singh
  • Published online:
    20 February 2026
    Print publication:
    26 March 2026
  • This tutorial guide introduces online nonstochastic control, an emerging paradigm in control of dynamical systems and differentiable reinforcement learning that applies techniques from online convex optimization and convex relaxations to obtain new methods with provable guarantees for classical settings in optimal and robust control. In optimal control, robust control, and other control methodologies that assume stochastic noise, the goal is to perform comparably to an offline optimal strategy. In online control, both cost functions and perturbations from the assumed dynamical model are chosen by an adversary. Thus, the optimal policy is not defined a priori and the goal is to attain low regret against the best policy in hindsight from a benchmark class of policies. The resulting methods are based on iterative mathematical optimization algorithms and are accompanied by finite-time regret and computational complexity guarantees. This book is ideal for graduate students and researchers interested in bridging classical control theory and modern machine learning.

Page 9 of 126