Not All Exploration Is Informative: Targeted Inference in Adaptive Experiments

Adaptive experiments must earn deployment reward while estimating prespecified contrasts. Regret theory asks how much exploration learning requires; adaptive-inference theory recovers valid uncertainty after history-dependent assignment. We ask which exploration informs the requested directions. Equal expected counts can produce arbitrarily different inverse-propensity variance, while equal welfare and scalar information can leave different target contrasts with sharply different precision. We develop clock-separated information flows (\CSIF). A base policy retains its decision clock, while a logged evaluation clock allocates a welfare-priced information portfolio across target directions. Structured acquisition matrices and the predictable quadratic variation for design-based inference remain separate information states. Finite-sample matrix concentration and clock transfer connect deployment to a deterministic reference. An independent Gaussian pilot followed by a frozen evaluation design gives a pilot-to-deployment certificate: under balanced-pilot and leverage conditions, pilot-induced design and reference-information drift scale as $m^{-1/2}$. Logged propensities give exact design unbiasedness, a finite-sample interval, and, under score regularity, a studentized limit. At a fixed Gaussian reference instance, a local two-point risk lower bound and rounded fixed-design attainability identify the geometric welfare price up to a universal constant. In -repetition synthetic studies, targeting reduces worst-target standard error by in the bandit model and in the linear model under matched evaluation schedules. Across train/held-out splits of a 64,000-customer randomized e-mail trial, it reduces prospective plug-in worst-contrast width by for a 12,000-customer experiment. Information is therefore a directionally allocated resource, not a pull-count total.