DeepAI AI Chat
Log In Sign Up

Thompson Sampling Guided Stochastic Searching on the Line for Deceptive Environments with Applications to Root-Finding Problems

by   Sondre Glimsdal, et al.
Universitetet Agder

The multi-armed bandit problem forms the foundation for solving a wide range of on-line stochastic optimization problems through a simple, yet effective mechanism. One simply casts the problem as a gambler that repeatedly pulls one out of N slot machine arms, eliciting random rewards. Learning of reward probabilities is then combined with reward maximization, by carefully balancing reward exploration against reward exploitation. In this paper, we address a particularly intriguing variant of the multi-armed bandit problem, referred to as the Stochastic Point Location (SPL) Problem. The gambler is here only told whether the optimal arm (point) lies to the "left" or to the "right" of the arm pulled, with the feedback being erroneous with probability 1-π. This formulation thus captures optimization in continuous action spaces with both informative and deceptive feedback. To tackle this class of problems, we formulate a compact and scalable Bayesian representation of the solution space that simultaneously captures both the location of the optimal arm as well as the probability of receiving correct feedback. We further introduce the accompanying Thompson Sampling guided Stochastic Point Location (TS-SPL) scheme for balancing exploration against exploitation. By learning π, TS-SPL also supports deceptive environments that are lying about the direction of the optimal arm. This, in turn, allows us to solve the fundamental Stochastic Root Finding (SRF) Problem. Empirical results demonstrate that our scheme deals with both deceptive and informative environments, significantly outperforming competing algorithms both for SRF and SPL.


page 1

page 2

page 3

page 4


Optimal Exploration-Exploitation in a Multi-Armed-Bandit Problem with Non-stationary Rewards

In a multi-armed bandit (MAB) problem a gambler needs to choose at each ...

Adaptive Algorithms for Multi-armed Bandit with Composite and Anonymous Feedback

We study the multi-armed bandit (MAB) problem with composite and anonymo...

Some performance considerations when using multi-armed bandit algorithms in the presence of missing data

When using multi-armed bandit algorithms, the potential impact of missin...

On Adaptive Estimation for Dynamic Bernoulli Bandits

The multi-armed bandit (MAB) problem is a classic example of the explora...

Arm order recognition in multi-armed bandit problem with laser chaos time series

By exploiting ultrafast and irregular time series generated by lasers wi...

Approximate information for efficient exploration-exploitation strategies

This paper addresses the exploration-exploitation dilemma inherent in de...

Dueling Bandits with Qualitative Feedback

We formulate and study a novel multi-armed bandit problem called the qua...