# Event

### CCSP Seminar: K. A. Sankararaman, "Adversarial Bandits with Knapsacks"

Thursday, March 14, 2019

5:00 p.m.-6:30 p.m.

AVW 2168

Ajaykrishnan Nageswaran

301 405 3661

ajayk@umd.edu

http://www.ece.umd.edu/seminars/ccsp/

Communication, Control and Signal Processing Seminar

Adversarial Bandits with Knapsacks

Karthik Abinav Sankararaman

University of Maryland

**Abstract**

In this talk, we will discuss the multi-armed bandits problem with resource constraints, in the adversarial setting. In this problem, we have an interactive and repeated game between the algorithm and an adversary. Given $T$ time-steps, $d$ resources, $m$ actions and budgets $B_1, B_2,\ldots B_d$, the algorithm chooses one of the $m$ actions at each time-step. An adversary then reveals a reward and consumption for each of the $d$ resources, corresponding to this action. The time-step at which the algorithm runs out of the $d$ resources (i.e., the total consumption for resource $j > B_j$), the game stops and the total reward is the sum of rewards obtained until the stopping time. The goal is to maximize the competitive ratio; the ratio of the total reward of the algorithm to the expected reward of a fixed distribution that knows the rewards and consumption for all actions and time-steps beforehand. We give an algorithm for this problem whose competitive ratio is tight (matches the lower-bound). The algorithm achieves the optimal bound, both in expectation and with high-probability. Moreover, the algorithmic framework is modular and can be used in a black-box manner to obtain algorithms to many related problems such as the stochastic, contextual, semi-bandit settings as well as to the more general online constrained convex optimization setting.

The talk is based on this paper.