A large-scale clinical trial has shown that even long-term consumption of DHA--an omega-3 fatty acid found in abundance in oily fish--may not lead to improvements in cognitive function. Docosahexaenoic acid (DHA), an omega-3 fatty acid found in abundance in oily fish such as mackerel and sardines, is thought to improve cognitive function by supporting connections between brain cells. However, it has never been conclusively demonstrated that DHA taken as a dietary supplement actually reaches the brain or provides measurable benefits against dementia . Against this backdrop, a research team at the USC School of Medicine has published the results of a large, two-year clinical trial involving older adults at elevated risk of developing Alzheimer's disease . The study found that while high-dose DHA supplements do indeed reach the brain, they did not improve memory or cognitive function, nor did they slow brain atrophy.

Response-adaptive randomization (RAR) in clinical trials aims to improve ethical and statistical efficiency by dynamically allocating patients to treatments based on observed outcomes. While RAR based on a target optimal allocation have been extensively studied for two-arms settings, their extension to multi-treatment experiments ($K \geq 2$) remains theoretically fragmented, with most existing methods focusing on specific algorithms or restricted target allocations. In this paper, we introduce a unified framework for response-adaptive targeting, the $α$-Rebalancing Targeting Strategies ($α$RTS), which generalize the ERADE two-armed strategy of Hu et al. [2009]. We prove that all designs in this family share fundamental asymptotic properties: strong consistency, asymptotic normality of allocation proportions and treatment effect estimators, and asymptotic efficiency. To address sparse target regimes (where some treatments are asymptotically eliminated), we further propose $α$RTS with Forced Exploration, a variant that guarantees infinite sampling for all treatments while preserving the asymptotic guarantees. Extensive simulations illustrate the finite-sample behavior of $α$RTS variants in a 3-armed context, highlighting in particular the critical role of forced exploration in sparse settings.

A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately.

Popular algorithms suchasUCB[4,5]andThompson sampling [3,34]typically explorethearms sufficiently and as more evidence is gathered, converge to the optimal arm.

Modeling dependencies in multivariate discrete data is a challenging problem, especiallyinhighdimensions.

In the following equation, we use the results inAppendix D.1 tocalculate the probability that there exists some arm whose mean value isaboveitsconfidence intervalofwidth