Online platforms increasingly compare many adaptive decision policies---ranking systems, recommendation algorithms, pricing rules, and language-model agents---while each reward-bearing interaction can be costly or risky. A direct A/B/n design gives each of $J$ policies its own horizon-$T$ trajectory and therefore uses $JT$ outcomes. We introduce Tree-Coupled A/B Testing (\TCAB), an exact feedback-sharing design for arbitrary history-dependent contextual-bandit policies. At each round, a predictable tree connects the current policy histories; every parent--child context--action law is maximally coupled, and one reward is shared within each component of matched tree edges. Every policy retains exactly its standalone finite-horizon trajectory law, even though the policies are deliberately dependent. If $D_{e,t}$ records a mismatch on tree edge $e$ at round $t$, the number of reward queries satisfies the pathwise identity $N(T)=T+\sum_{t,e}D_{e,t}$ and hence equals $T$ plus cumulative tree-edge total variation in expectation. This cost is conditionally optimal among exact edge-local designs on the selected tree, and a current-round minimum-spanning tree is myopically optimal among tree designs. For fixed $J$, sublinear pseudo-regret of every policy and almost-sure uniqueness of the oracle action imply $\mathbb{E}[N(T)]=T+o(T)$, versus $JT$ for independent runs. We also obtain finite-sample variance bounds for pairwise policy contrasts. Experiments on reward-model evaluation, multiple-choice language-model evaluation, and adaptive search policies demonstrate substantial improvements in the cost--precision frontier.
Min Zeng, Yichen Zhang, Xiaofeng Shaostat.ML cs.LG
Constant-stepsize temporal-difference (TD) learning is attractive for policy evaluation, but inference from a single Markov trajectory must account for serial dependence and a stepsize-dependent stationary target. For fixed-stepsize linear TD, we establish a functional central limit theorem whose covariance retains the multiplicative component induced by the random TD matrix and the stationary iterate error. We then derive a joint functional limit for parallel Richardson--Romberg (RR) recursions driven by the same trajectory. A Brownian-bridge self-normalizer yields asymptotically pivotal confidence regions for prespecified state-value contrasts without estimating the long-run covariance or selecting a bandwidth or batch length. For such a contrast, the procedure admits a one-pass implementation whose memory does not grow with the trajectory length. At a fixed stepsize, the inferential center is the RR stationary target. We also study horizon-indexed designs in which the stepsize remains constant within each run and decreases across longer horizons. Under an explicit RR-dependent rate window, the residual RR target shift, multiplicative remainder, and initialization effect are negligible at the root-$n$ scale, yielding inference for the projected Bellman solution. Experiments on FrozenLake and Garnet illustrate stationary-target coverage, RR target correction, and the finite-sample behavior of the horizon-indexed design.
From medicine to marketing to social sciences, the promise of tailoring interventions to individuals is undeniable. However, practical applications force weighing personalization's potential benefits with its possible increased cost and fragility. We introduce a statistical hypothesis test that evaluates, given historical data, evidence that a personalized intervention policy's performance will surpass deploying the best single intervention. The test maintains strict type-I error control while achieving asymptotic normality with the minimal possible variance under specified conditions. Results on diverse datasets from job training, depression treatment, education and recommendation systems demonstrate the test's versatility and its superior performance over alternatives. This test can support decision-makers throughout the intervention sciences by providing a simple and powerful quantification of the potential benefits of personalization.