Be Greedy in Multi-Armed Bandits

by   Matthieu Jedor, et al.

The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known to sometimes have poor performances, for instance even a linear regret (with respect to the time horizon) in the standard multi-armed bandit problem. On the other hand, this heuristic performs reasonably well in practice and it even has sublinear, and even near-optimal, regret bounds in some very specific linear contextual and Bayesian bandit models. We build on a recent line of work and investigate bandit settings where the number of arms is relatively large and where simple greedy algorithms enjoy highly competitive performance, both in theory and in practice. We first provide a generic worst-case bound on the regret of the Greedy algorithm. When combined with some arms subsampling, we prove that it verifies near-optimal worst-case regret bounds in continuous, infinite and many-armed bandit problems. Moreover, for shorter time spans, the theoretical relative suboptimality of Greedy is even reduced. As a consequence, we subversively claim that for many interesting problems and associated horizons, the best compromise between theoretical guarantees, practical performances and computational burden is definitely to follow the greedy heuristic. We support our claim by many numerical experiments that show significant improvements compared to the state-of-the-art, even for moderately long time horizon.


Optimal and Greedy Algorithms for Multi-Armed Bandits with Many Arms

We characterize Bayesian regret in a stochastic multi-armed bandit probl...

Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

When confronted with massive data streams, summarizing data with dimensi...

Distributed Bandit Learning: How Much Communication is Needed to Achieve (Near) Optimal Regret

We study the communication complexity of distributed multi-armed bandits...

AC-Band: A Combinatorial Bandit-Based Approach to Algorithm Configuration

We study the algorithm configuration (AC) problem, in which one seeks to...

Finding the Bandit in a Graph: Sequential Search-and-Stop

We consider the problem where an agent wants to find a hidden object tha...

Contextual Multi-armed Bandits under Feature Uncertainty

We study contextual multi-armed bandit problems under linear realizabili...

Tractable Optimality in Episodic Latent MABs

We consider a multi-armed bandit problem with M latent contexts, where a...

Please sign up or login with your details

Forgot password? Click here to reset