Contextual bandits with concave rewards, and an application to fair ranking

by   Virginie Do, et al.

We consider Contextual Bandits with Concave Rewards (CBCR), a multi-objective bandit problem where the desired trade-off between the rewards is defined by a known concave objective function, and the reward vector depends on an observed stochastic context. We present the first algorithm with provably vanishing regret for CBCR without restrictions on the policy space, whereas prior works were restricted to finite policy spaces or tabular representations. Our solution is based on a geometric interpretation of CBCR algorithms as optimization algorithms over the convex set of expected rewards spanned by all stochastic policies. Building on Frank-Wolfe analyses in constrained convex optimization, we derive a novel reduction from the CBCR regret to the regret of a scalar-reward bandit problem. We illustrate how to apply the reduction off-the-shelf to obtain algorithms for CBCR with both linear and general reward functions, in the case of non-combinatorial actions. Motivated by fairness in recommendation, we describe a special case of CBCR with rankings and fairness-aware objectives, leading to the first algorithm with regret guarantees for contextual combinatorial bandits with fairness of exposure.


page 1

page 2

page 3

page 4


Fairness of Exposure in Stochastic Bandits

Contextual bandit algorithms have become widely used for recommendation ...

Fairness in Learning: Classic and Contextual Bandits

We introduce the study of fairness in multi-armed bandit problems. Our f...

Group Meritocratic Fairness in Linear Contextual Bandits

We study the linear contextual bandit problem where an agent has to sele...

Contextual Bandits and Optimistically Universal Learning

We consider the contextual bandit problem on general action and context ...

The Combinatorial Multi-Bandit Problem and its Application to Energy Management

We study a Combinatorial Multi-Bandit Problem motivated by applications ...

Restless Hidden Markov Bandits with Linear Rewards

This paper presents an algorithm and regret analysis for the restless hi...

Semiparametric Contextual Bandits

This paper studies semiparametric contextual bandits, a generalization o...

Please sign up or login with your details

Forgot password? Click here to reset