Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning.

Wederiveinstance specific nonasymptotic and asymptotic lower bounds which generalize those of theIIDsetting.

We determine the sample complexity of pure exploration bandit problems with multiple goodanswers.

In the evolving landscape of high-speed agile quadrotor flight, achieving precise trajectory tracking at the platform's operational limits is paramount. Controllers must handle actuator constraints, exhibit robustness to disturbances, and remain computationally efficient for safety-critical applications. In this work, we present a novel neural-augmented feedback controller for agile flight control. The controller addresses individual limitations of existing state-of-the-art control paradigms and unifies their strengths. We demonstrate the controller's capabilities, including the accurate tracking of highly aggressive trajectories that surpass the feasibility of the actuators. Notably, the controller provides universal stability guarantees, enhancing its robustness and tracking performance even in exceedingly disturbance-prone settings. Its nonlinear feedback structure is highly efficient enabling fast computation at high update rates. Moreover, the learning process in simulation is both fast and stable, and the controller's inherent robustness allows direct deployment to real-world platforms without the need for training augmentations or fine-tuning.

Motivated by recursive learning in Markov Decision Processes, this paper studies best-arm identification in bandit problems where each arm's reward is drawn from a multinomial distribution with a known support. We compare the performance { reached by strategies including notably LUCB without and with use of this knowledge. } In the first case, we use classical non-parametric approaches for the confidence intervals. In the second case, where a probability distribution is to be estimated, we first use classical deviation bounds (Hoeffding and Bernstein) on each dimension independently, and then the Empirical Likelihood method (EL-LUCB) on the joint probability vector. The effectiveness of these methods is demonstrated through simulations on scenarios with varying levels of structural complexity.

We introduce the problem of best arm identification (BAI) with post-action context, a new BAI problem in a stochastic multi-armed bandit environment and the fixed-confidence setting. The problem addresses the scenarios in which the learner receives a $\textit{post-action context}$ in addition to the reward after playing each action. This post-action context provides additional information that can significantly facilitate the decision process. We analyze two different types of the post-action context: (i) $\textit{non-separator}$, where the reward depends on both the action and the context, and (ii) $\textit{separator}$, where the reward depends solely on the context. For both cases, we derive instance-dependent lower bounds on the sample complexity and propose algorithms that asymptotically achieve the optimal sample complexity. For the non-separator setting, we do so by demonstrating that the Track-and-Stop algorithm can be extended to this setting. For the separator setting, we propose a novel sampling rule called $\textit{G-tracking}$, which uses the geometry of the context space to directly track the contexts rather than the actions. Finally, our empirical results showcase the advantage of our approaches compared to the state of the art.

A Multi Armed Bandit (MAB) is a model of a sequential interaction that was introduced in (Thompson, 1933) to create better medical trials. This framework has since been expanded to various fields, and has seen applications to online advertising and recommendation systems. In a MAB, an algorithm chooses at each time an arm among a finite number (it pulls it) and then observes a sample from a probability distribution associated with the arm. The goal of the interaction will be to identify quickly which arm has the distribution with highest mean. By making use of past observed rewards to continuously update the way they sample, MAB algorithms reach their objective faster than traditional fixed randomized trials. For applications like online advertising, obtaining feedback can be quick, if for example the feedback is a click on an advertisement.

We study the fixed-confidence best-arm identification problem in unimodal bandits, in which the means of the arms increase with the index of the arm up to their maximum, then decrease. We derive two lower bounds on the stopping time of any algorithm. The instance-dependent lower bound suggests that due to the unimodal structure, only three arms contribute to the leading confidence-dependent cost. However, a worst-case lower bound shows that a linear dependence on the number of arms is unavoidable in the confidence-independent cost. We propose modifications of Track-and-Stop and a Top Two algorithm that leverage the unimodal structure. Both versions of Track-and-Stop are asymptotically optimal for one-parameter exponential families. The Top Two algorithm is asymptotically near-optimal for Gaussian distributions and we prove a non-asymptotic guarantee matching the worse-case lower bound. The algorithms can be implemented efficiently and we demonstrate their competitive empirical performance.

Time-optimal obstacle avoidance is a prevalent problem encountered in various fields, including robotics and autonomous vehicles, where the task involves determining a path for a moving vehicle to reach its goal while navigating around obstacles within its environment. This problem becomes increasingly challenging as the number of obstacles in the environment rises. We propose an iterative active-inactive obstacle approach, which involves identifying a subset of the obstacles as "active", that considers solely the effect of the "active" obstacles on the path of the moving vehicle. The remaining obstacles are considered "inactive" and are not considered in the path planning process. The obstacles are classified as 'active' on the basis of previous findings derived from prior iterations. This approach allows for a more efficient calculation of the optimal path by reducing the number of obstacles that need to be considered. The effectiveness of the proposed method is demonstrated with two different dynamic models using the various number of obstacles. The results show that the proposed method is able to find the optimal path in a timely manner, while also being able to handle a large number of obstacles in the environment and the constraints on the motion of the object.

We consider the fixed-confidence best arm identification (FC-BAI) problem in the Bayesian Setting. This problem aims to find the arm of the largest mean with a fixed confidence level when the bandit model has been sampled from the known prior. Most studies on the FC-BAI problem have been conducted in the frequentist setting, where the bandit model is predetermined before the game starts. We show that the traditional FC-BAI algorithms studied in the frequentist setting, such as track-and-stop and top-two algorithms, result in arbitrary suboptimal performances in the Bayesian setting. We also prove a lower bound of the expected number of samples in the Bayesian setting and introduce a variant of successive elimination that has a matching performance with the lower bound up to a logarithmic factor. Simulations verify the theoretical results.