Pure Exploration with Multiple Correct Answers

We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexity. However, that convexity is lost when going to the multiple-answer setting. We present a new algorithm which extends Track-and-Stop to the multiple-answer case and has asymptotic sample complexity matching the lower bound

The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime

We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how difficult it is to distinguish a good sampling strategy from a bad one given the limited amount of data collected up to any given time. This change of perspective allows us to match the strength of both Fano and change-of-measure techniques, without succumbing to the limitations of either method. For concreteness, we apply our techniques to a structured multi-arm bandit problem in the fixed-confidence pure exploration setting, where we show that the constraints on the means imply a substantial gap between the moderate-confidence sample complexity, and the asymptotic sample complexity as $\delta \to 0$ found in the literature. We also prove the first instance-based lower bounds for the top-k problem which incorporate the appropriate log-factors. Moreover, our lower bounds zero-in on the number of times each \emph{individual} arm needs to be pulled, uncovering new phenomena which are drowned out in the aggregate sample complexity. Our new analysis inspires a simple and near-optimal algorithm for the best-arm and top-k identification, the first {\em practical} algorithm of its kind for the latter problem which removes extraneous log factors, and outperforms the state-of-the-art in experiments

Social Competence Treatment after Traumatic Brain Injury: A Multicenter, Randomized, Controlled Trial of Interactive Group Treatment versus Non-Interactive Treatment

Objective To evaluate the effectiveness of a replicable group treatment program for improving social competence after traumatic brain injury (TBI). Design Multicenter randomized controlled trial comparing two methods of conducting a social competency skills program, an interactive group format versus a classroom lecture. Setting Community and Veteran rehabilitation centers. Participants 179 civilian, military, and veteran adults with TBI and social competence difficulties, at least 6 months post-injury. Experimental Intervention Thirteen weekly group interactive sessions (1.5 hours) with structured and facilitated group interactions to improve social competence. Alternative (Control) Intervention Thirteen traditional classroom sessions using the same curriculum with brief supplemental individual sessions but without structured group interaction. Primary Outcome Measure Profile of Pragmatic Impairment in Communication (PPIC), an objective behavioral rating of social communication impairments following TBI. Secondary Outcomes LaTrobe Communication Questionnaire (LCQ), Goal Attainment Scale (GAS), Satisfaction with Life Scale (SWLS), Post-Traumatic Stress Disorder Checklist – (PCL-C), Brief Symptom Inventory 18 (BSI-18), Scale of Perceived Social Self Efficacy (PSSE). Results Social competence goals (GAS) were achieved and maintained for most participants regardless of treatment method. Significant improvements in the primary outcome (PPIC) and two of the secondary outcomes (LCQ and BSI) were seen immediately post-treatment and at 3 months post-treatment in the AT arm only, however these improvements were not significantly different between the GIST and AT arms. Similar trends were observed for PSSE and PCL-C. Conclusions Social competence skills improved for persons with TBI in both treatment conditions. The group interactive format was not found to be a superior method of treatment delivery in this study