Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, September 20, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Maxime Larcher

A Random Walk Algorithm for the 2-Armed Bandit

In the 2-Armed Bandit Problem, an agent faces two slots machines. At round 1, 2, ..., T the agent pulls the arm of their choice and receives a random reward, sampled according to the (hidden) distribution of that arm. Naturally, the goal of the agent is to minimise the total regret, i.e. the total expected missed reward over the T rounds.

When the reward distribution is allowed to change up to L times over the T rounds (without the agent knowing when such changes happen), it was shown by Auer et al. '02 that no algorithm can achieve regret better than Ω((LT)^1/2). In 2019, Auer et al. used Azuma's inequality to bound the probability of 'bad events' and presented an algorithm achieving regret O((LT log T)^1/2).

We present a new algorithm based on random walks and which achieves regret O((LT)^1/2) when L is known and O((LT log L)^1/2) when L is unknown. In particular, our algorithm is optimal when L is known. We also obtain improved bounds for the general K-Armed bandit for a wide range of K.

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