Reward Maximization for Pure Exploration: Minimax Optimal Good Arm Identification for Nonparametric Multi-Armed Bandits

In multi-armed bandits, the tasks of reward maximization and pure exploration are often at odds with each other. The former focuses on exploiting arms with the highest means, while the latter may require constant exploration across all arms. In this work, we focus on good arm identification (GAI), a practical bandit inference objective that aims to label arms with means above a threshold as quickly as possible. We show that GAI can be efficiently solved by combining a reward-maximizing sampling algorithm with a novel nonparametric anytime-valid sequential test for labeling arm means. We first establish that our sequential test maintains error control under highly nonparametric assumptions and asymptotically achieves the minimax optimal e-power, a notion of power for anytime-valid tests. Next, by pairing regret-minimizing sampling schemes with our sequential test, we provide an approach that achieves minimax optimal stopping times for labeling arms with means above a threshold, under an error probability constraint. Our empirical results validate our approach beyond the minimax setting, reducing the expected number of samples for all stopping times by at least 50% across both synthetic and real-world settings.

Towards Human Understanding of Paraphrase Types in ChatGPT

Paraphrases represent a human's intuitive ability to understand expressions presented in various different ways. Current paraphrase evaluations of language models primarily use binary approaches, offering limited interpretability of specific text changes. Atomic paraphrase types (APT) decompose paraphrases into different linguistic changes and offer a granular view of the flexibility in linguistic expression (e.g., a shift in syntax or vocabulary used). In this study, we assess the human preferences towards ChatGPT in generating English paraphrases with ten APTs and five prompting techniques. We introduce APTY (Atomic Paraphrase TYpes), a dataset of 500 sentence-level and word-level annotations by 15 annotators. The dataset also provides a human preference ranking of paraphrases with different types that can be used to fine-tune models with RLHF and DPO methods. Our results reveal that ChatGPT can generate simple APTs, such as additions and deletions, but struggle with complex structures (e.g., subordination changes). This study contributes to understanding which aspects of paraphrasing language models have already succeeded at understanding and what remains elusive. In addition, our curated datasets can be used to develop language models with specific linguistic capabilities.

Designing and evaluating an online reinforcement learning agent for physical exercise recommendations in N-of-1 trials

Personalized adaptive interventions offer the opportunity to increase patient benefits, however, there are challenges in their planning and implementation. Once implemented, it is an important question whether personalized adaptive interventions are indeed clinically more effective compared to a fixed gold standard intervention. In this paper, we present an innovative N-of-1 trial study design testing whether implementing a personalized intervention by an online reinforcement learning agent is feasible and effective. Throughout, we use a new study on physical exercise recommendations to reduce pain in endometriosis for illustration. We describe the design of a contextual bandit recommendation agent and evaluate the agent in simulation studies. The results show that adaptive interventions add complexity to the design and implementation process, but have the potential to improve patients' benefits even if only few observations are available. In order to quantify the expected benefit, data from previous interventional studies is required. We expect our approach to be transferable to other interventions and clinical interventions.