Upper Confidence Bound (UCB) methods are one of the most effective methods in dealing with the exploration-exploitation trade-off in online decision-making problems. The confidence bounds utilized in UCB methods tend to be constructed based on concentration equalities which are usually dependent on a parameter of scale (e.g. a bound on the payoffs, a variance, or a subgaussian parameter) that must be known in advance. The necessity of knowing a scale parameter a priori and the fact that the confidence bounds only use the tail information can deteriorate the performance of the UCB methods.Here we propose a data-dependent UCB algorithm called MARS (Maximum Average Randomly Sampled) in a non-parametric setup for multi-armed bandits with symmetric rewards. The algorithm does not depend on any scaling, and the data-dependent upper confidence bound is constructed based on the maximum average of randomly sampled rewards inspired by the work of Hartigan in the 1960s and 70s. A regret bound for the multi-armed bandit problem is derived under the same assumptions as for the $\psi$-UCB method without incorporating any correction factors. The method is illustrated and compared with baseline algorithms in numerical experiments.

Upper Confidence Bound (UCB) methods are one of the most effective methods in dealing with the exploration-exploitation trade-off in online decision-making problems. The confidence bounds utilized in UCB methods tend to be constructed based on concentration equalities which are usually dependent on a parameter of scale (e.g. a bound on the payoffs, a variance, or a subgaussian parameter) that must be known in advance. The necessity of knowing a scale parameter a priori and the fact that the confidence bounds only use the tail information can deteriorate the performance of the UCB methods.Here we propose a data-dependent UCB algorithm called MARS (Maximum Average Randomly Sampled) in a non-parametric setup for multi-armed bandits with symmetric rewards. The algorithm does not depend on any scaling, and the data-dependent upper confidence bound is constructed based on the maximum average of randomly sampled rewards inspired by the work of Hartigan in the 1960s and 70s. A regret bound for the multi-armed bandit problem is derived under the same assumptions as for the \psi -UCB method without incorporating any correction factors.

Recently, Large Language Models (LLMs) have been widely studied by researchers for their roles in various downstream NLP tasks. As a fundamental task in the NLP field, Chinese Grammatical Error Correction (CGEC) aims to correct all potential grammatical errors in the input sentences. Previous studies have shown that LLMs' performance as correctors on CGEC remains unsatisfactory due to its challenging task focus. To promote the CGEC field to better adapt to the era of LLMs, we rethink the roles of LLMs in the CGEC task so that they can be better utilized and explored in CGEC. Considering the rich grammatical knowledge stored in LLMs and their powerful semantic understanding capabilities, we utilize LLMs as explainers to provide explanation information for the CGEC small models during error correction to enhance performance. We also use LLMs as evaluators to bring more reasonable CGEC evaluations, thus alleviating the troubles caused by the subjectivity of the CGEC task. In particular, our work is also an active exploration of how LLMs and small models better collaborate in downstream tasks. Extensive experiments and detailed analyses on widely used datasets verify the effectiveness of our thinking intuition and the proposed methods.

We focus on the problem of long-range dynamic replanning for off-road autonomous vehicles, where a robot plans paths through a previously unobserved environment while continuously receiving noisy local observations. An effective approach for planning under sensing uncertainty is determinization, where one converts a stochastic world into a deterministic one and plans under this simplification. This makes the planning problem tractable, but the cost of following the planned path in the real world may be different than in the determinized world. This causes collisions if the determinized world optimistically ignores obstacles, or causes unnecessarily long routes if the determinized world pessimistically imagines more obstacles. We aim to be robust to uncertainty over potential worlds while still achieving the efficiency benefits of determinization. We evaluate algorithms for dynamic replanning on a large real-world dataset of challenging long-range planning problems from the DARPA RACER program. Our method, Dynamic Replanning via Evaluating and Aggregating Multiple Samples (DREAMS), outperforms other determinization-based approaches in terms of combined traversal time and collision cost. https://sites.google.com/cs.washington.edu/dreams/

We formulate the problem of eliciting agents' preferences with the goal of finding a Kemeny ranking as a Dueling Bandits problem. Here the bandits' arms correspond to alternatives that need to be ranked and the feedback corresponds to a pairwise comparison between alternatives by a randomly sampled agent. We consider both sampling with and without replacement, i.e., the possibility to ask the same agent about some comparison multiple times or not. We find approximation bounds for Kemeny rankings dependant on confidence intervals over estimated winning probabilities of arms. Based on these we state algorithms to find Probably Approximately Correct (PAC) solutions and elaborate on their sample complexity for sampling with or without replacement. Furthermore, if all agents' preferences are strict rankings over the alternatives, we provide means to prune confidence intervals and thereby guide a more efficient elicitation. We formulate several adaptive sampling methods that use look-aheads to estimate how much confidence intervals (and thus approximation guarantees) might be tightened. All described methods are compared on synthetic data.

Image segmentation and registration are said to be challenging when applied to dynamic contrast enhanced MRI sequences (DCE-MRI). The contrast agent causes rapid changes in intensity in the region of interest and elsewhere, which can lead to false positive predictions for segmentation tasks and confound the image registration similarity metric. While it is widely assumed that contrast changes increase the difficulty of these tasks, to our knowledge no work has quantified these effects. In this paper we examine the effect of training with different ratios of contrast enhanced (CE) data on two popular tasks: segmentation with nnU-Net and Mask R-CNN and registration using VoxelMorph and VTN. We experimented further by strategically using the available datasets through pretraining and fine tuning with different splits of data. We found that to create a generalisable model, pretraining with CE data and fine tuning with non-CE data gave the best result. This interesting find could be expanded to other deep learning based image processing tasks with DCE-MRI and provide significant improvements to the models performance.