The objective of canonical multi-armed bandits is to identify and repeatedly select an arm with the largest reward, often in the form of the expected value of the arm's probability distribution. Such a utilitarian perspective and focus on the probability models' first moments, however, is agnostic to the distributions' tail behavior and their implications for variability and risks in decision-making. This paper introduces a principled framework for shifting from expectation-based evaluation to an alternative reward formulation, termed a preference metric (PM). The PMs can place the desired emphasis on different reward realization and can encode a richer modeling of preferences that incorporate risk aversion, robustness, or other desired attitudes toward uncertainty. A fundamentally distinct observation in such a PM-centric perspective is that designing bandit algorithms will have a significantly different principle: as opposed to the reward-based models in which the optimal sampling policy converges to repeatedly sampling from the single best arm, in the PM-centric framework the optimal policy converges to selecting a mix of arms based on specific mixing weights. Designing such mixture policies departs from the principles for designing bandit algorithms in significant ways, primarily because of uncountable mixture possibilities. The paper formalizes the PM-centric framework and presents two algorithm classes (horizon-dependent and anytime) that learn and track mixtures in a regret-efficient fashion. These algorithms have two distinctions from their canonical counterparts: (i) they involve an estimation routine to form reliable estimates of optimal mixtures, and (ii) they are equipped with tracking mechanisms to navigate arm selection fractions to track the optimal mixtures. These algorithms' regret guarantees are investigated under various algebraic forms of the PMs.

Markov decision processes (MDP) are a well-established model for sequential decision-making in the presence of probabilities. In robust MDP (RMDP), every action is associated with an uncertainty set of probability distributions, modelling that transition probabilities are not known precisely. Based on the known theoretical connection to stochastic games, we provide a framework for solving RMDPs that is generic, reliable, and efficient. It is *generic* both with respect to the model, allowing for a wide range of uncertainty sets, including but not limited to intervals, $L^1$- or $L^2$-balls, and polytopes; and with respect to the objective, including long-run average reward, undiscounted total reward, and stochastic shortest path. It is *reliable*, as our approach not only converges in the limit, but provides precision guarantees at any time during the computation. It is *efficient* because -- in contrast to state-of-the-art approaches -- it avoids explicitly constructing the underlying stochastic game. Consequently, our prototype implementation outperforms existing tools by several orders of magnitude and can solve RMDPs with a million states in under a minute.

In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances.

Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known anytime search algorithms are based on best-first search. In this paper, we propose a new algorithm, rectangle search, that is instead based on beam search, a variant of breadth-first search. It repeatedly explores alternatives at all depth levels and is thus best-suited to problems featuring deep local minima. Experiments using a variety of popular search benchmarks suggest that rectangle search is competitive with fixed-width beam search and often performs better than the previous best anytime search algorithms.

Grasping moving objects is a challenging task that requires multiple submodules such as object pose predictor, arm motion planner, etc. Each submodule operates under its own set of meta-parameters. For example, how far the pose predictor should look into the future (i.e., look-ahead time) and the maximum amount of time the motion planner can spend planning a motion (i.e., time budget). Many previous works assign fixed values to these parameters; however, at different moments within a single episode of dynamic grasping, the optimal values should vary depending on the current scene. In this work, we propose a dynamic grasping pipeline with a meta-controller that controls the look-ahead time and time budget dynamically. We learn the meta-controller through reinforcement learning with a sparse reward. Our experiments show the meta-controller improves the grasping success rate (up to 28% in the most cluttered environment) and reduces grasping time, compared to the strongest baseline. Our meta-controller learns to reason about the reachable workspace and maintain the predicted pose within the reachable region. In addition, it assigns a small but sufficient time budget for the motion planner. Our method can handle different objects, trajectories, and obstacles. Despite being trained only with 3-6 random cuboidal obstacles, our meta-controller generalizes well to 7-9 obstacles and more realistic out-of-domain household setups with unseen obstacle shapes.

In good arm identification (GAI), the goal is to identify one arm whose average performance exceeds a given threshold, referred to as good arm, if it exists. Few works have studied GAI in the fixed-budget setting, when the sampling budget is fixed beforehand, or the anytime setting, when a recommendation can be asked at any time. We propose APGAI, an anytime and parameter-free sampling rule for GAI in stochastic bandits. APGAI can be straightforwardly used in fixed-confidence and fixed-budget settings. First, we derive upper bounds on its probability of error at any time. They show that adaptive strategies are more efficient in detecting the absence of good arms than uniform sampling. Second, when APGAI is combined with a stopping rule, we prove upper bounds on the expected sampling complexity, holding at any confidence level. Finally, we show good empirical performance of APGAI on synthetic and real-world data. Our work offers an extensive overview of the GAI problem in all settings.

Anytime search algorithms are useful for planning problems where a solution is desired under a limited time budget. Anytime algorithms first aim to provide a feasible solution quickly and then attempt to improve it until the time budget expires. On the other hand, parallel search algorithms utilize the multithreading capability of modern processors to speed up the search. One such algorithm, ePA*SE (Edge-Based Parallel A* for Slow Evaluations), parallelizes edge evaluations to achieve faster planning and is especially useful in domains with expensive-to-compute edges. In this work, we propose an extension that brings the anytime property to ePA*SE, resulting in A-ePA*SE. We evaluate A-ePA*SE experimentally and show that it is significantly more efficient than other anytime search methods. The open-source code for A-ePA*SE, along with the baselines, is available here: https://github.com/shohinm/parallel_search

Prediction with experts' advice is one of the most fundamental problems in online learning and captures many of its technical challenges. A recent line of work has looked at online learning through the lens of differential equations and continuous-time analysis. This viewpoint has yielded optimal results for several problems in online learning. In this paper, we employ continuous-time stochastic calculus in order to study the discrete-time experts' problem. We use these tools to design a continuous-time, parameter-free algorithm with improved guarantees for the quantile regret. We then develop an analogous discrete-time algorithm with a very similar analysis and identical quantile regret bounds. Finally, we design an anytime continuous-time algorithm with regret matching the optimal fixed-time rate when the gains are independent Brownian Motions; in many settings, this is the most difficult case. This gives some evidence that, even with adversarial gains, the optimal anytime and fixed-time regrets may coincide.