It is well-known that obtaining sublinear regret in this setting is impossible in general, which arises the question of when can we do better than linear regret?

This problem faithfully models a natural revenue management problem, called "markdown pricing",

We first introduce a few notations.

We study a multi-armed bandit problem where the rewards exhibit regime switching.

Abstract-- In this work, we introduce BBoE, a bidirectional, kinodynamic, sampling-based motion planner that consistently and quickly finds low-cost solutions in environments with varying obstacle clutter . The algorithm combines exploration and exploitation while relying on precomputed robot state traversals, resulting in efficient convergence towards the goal. Our key contributions include: i) a strategy to navigate through obstacle-rich spaces by sorting and sequencing preprocessed forward propagations; and ii) BBoE, a robust bidirectional kinodynamic planner that utilizes this strategy to produce fast and feasible solutions. The proposed framework reduces planning time, diminishes solution cost and increases success rate in comparison to previous approaches. I. INTRODUCTION Motion planning in robotics involves identifying a series of valid configurations that a robot can assume to transition from an initial state to a desired goal state. Sampling-based planning is a popular graph-based approach used to generate robot motions by sampling discrete states and establishing connections between them via edges [23]. Their popularity is due to the inherent property of probabilistic completeness, which guarantees that a solution will be found, if one exists, as the number of sampled states reaches infinity [17], [10]. Traditionally, these techniques employ a unidirectional tree that grows from the start state and expands towards the goal region [17], [10], [6].

Automatic bidding has become one of the main options for advertisers to buy advertisement opportunities in the online advertising market [Dolan, 2020].