• Corpus ID: 252873694

Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications

  title={Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications},
  author={Daniel Lee and Georgy Noarov and Mallesh M. Pai and Aaron Roth},
We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. Even though the learner’s objective is not convex-concave (and so the minimax theorem does not apply), we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our framework by using it to (re)derive optimal bounds and e… 



Online Learning: Beyond Regret

This framework simultaneously captures such well-known notions as internal and general regret, learning with non-additive global cost functions, Blackwell’s approachability, calibration of forecasters, and more and shows that learnability in all these situations is due to control of the same three quantities.

Efficient learning algorithms for changing environments

A different performance metric is proposed which strengthens the standard metric of regret and measures performance with respect to a changing comparator and can be applied to various learning scenarios, i.e. online portfolio selection, for which there are experimental results showing the advantage of adaptivity.

Relax and Randomize : From Value to Algorithms

A principled way of deriving online learning algorithms from a minimax analysis is shown, including a family of randomized methods that use the idea of a "random playout" and new versions of the Follow-the-Perturbed-Leader algorithms.

Exponential Weight Approachability, Applications to Calibration and Regret Minimization

Basic ideas behind the “exponential weight algorithm” (designed for aggregation or minimization of regret) can be transposed into the theory of Blackwell approachability, and an algorithm is developed bounding the distance of average vector payoffs to some product set, with a logarithmic dependency in the dimension of the ambient space.

Approachability in unknown games: Online learning meets multi-objective optimization

It is shown that it is impossible, in general, to approach the best target set in hindsight and a concrete strategy to approach these goals is proposed.

Regret bounds for sleeping experts and bandits

This work compares algorithms against the payoff obtained by the best ordering of the actions, which is a natural benchmark for this type of problem and gives algorithms achieving information-theoretically optimal regret bounds with respect to the best-ordering benchmark.

Approachability, fast and slow

A characterization for the convergence rates of approachability is provided and it is shown that in some cases a set can be approached with a 1=n rate.

Multi-group Agnostic PAC Learnability

This work unify and extend previous positive and negative results from the multi-group fairness literature, which applied for specific loss functions, to study “multi-group agnostic PAC learnability”.

Set-valued approachability and online learning with partial monitoring

A variant of approachability is developed for games where there is ambiguity in the obtained reward: it belongs to a set rather than being a single vector and a simple and generally efficient strategy is developed.

Sequential decision making with vector outcomes

We study a multi-round optimization setting in which in each round a player may select one of several actions, and each action produces an outcome vector, not observable to the player until the round