The surrogate arrives too late to change the action
Each round follows the order context, action, surrogate, then a decision about whether to acquire the primary outcome. By the time the surrogate arrives, the action is already fixed, so the surrogate cannot revise it. What it can still change is whether the costly primary outcome that defines action value and regret is measured at all.
This is the paper's central distinction. The surrogate is not a substitute reward and does not redefine regret; action value and cumulative regret remain tied to the primary outcome. The surrogate is acquisition-side information: it helps decide where a limited measurement budget is spent, while the primary outcome continues to define what the learner is trying to optimize.
The paper frames the round as context, action, surrogate, acquisition decision, and only then the observed primary outcome. The acquisition decision determines whether the primary outcome is observed; it does not change future contexts or outcomes. That passivity is a scope condition, not a general claim about measurement.
Decision relevance and residual uncertainty both matter
The paper argues that the value of measuring the primary outcome depends on two separate quantities. Decision relevance asks how much the current outcome matters for unresolved comparisons between policies: if competing policies choose the same action, observing the primary outcome does not distinguish them on that round. Residual uncertainty asks how much variation remains after the surrogate is seen: if policies disagree but little residual variation remains, the primary outcome adds little for distinguishing them.
These two ingredients are used at different times. Before the surrogate is observed, the method sets a pre-surrogate acquisition level from decision relevance. After the surrogate is observed, it redistributes that level using an estimate of residual uncertainty, specifically a learned root-mean-square residual score for the primary outcome minus a fitted bridge.
The paper's explanation for this split comes from a variance decomposition of the policy-comparison evidence. The acquisition probability divides a term involving the squared policy-comparison coefficient and the residual variance, which is why relevance sets the level and residual uncertainty reallocates it across surrogate values.
A hard budget with an unbiased augmented update
The Audited Surrogate Bandit learns a contextual policy over a finite class of N deterministic policies while allocating a hard budget of B primary-outcome acquisitions across T rounds. The paper states that the method acquires exactly B primary outcomes on every path, using remaining-budget and remaining-round rules rather than an expected budget.
Selective measurement could bias an uncorrected policy update, so the method uses augmented feedback: a fitted bridge plus an inverse-acquisition-probability correction applied to the residual between the observed primary outcome and the bridge. Under the stated conditional independence of the acquisition draw and the primary outcome given history and the post-surrogate state, this correction preserves the primary-outcome conditional mean. The paper notes that the worst-case guarantee does not require the fitted bridge, residual score, or surrogate law to be correct; errors in them can hurt how efficiently the budget is used without changing the primary target preserved by the augmented update.
Policy weights are then updated with a second-order exponential-weights rule, and the bridge, residual score, and conditional surrogate law are refit online. The paper gives one concrete online fitting specification in an appendix.
Regret scales with the square root of T over B
For a finite class of N policies over K actions, the paper reports that the method incurs regret of order sqrt(KT log N) times (1 + sqrt(T/B)) relative to the best policy in the class, up to logarithmic factors. The budget B appears inside a square-root penalty, so a smaller acquisition budget makes the guarantee worse.
The paper also states a lower bound: the sqrt(T/B) dependence on the acquisition budget is unavoidable up to logarithmic factors on a subclass where an optimal policy is represented. This is a worst-case statement about the budget penalty, not a claim that every problem with a small budget behaves identically.
The paper's discussion adds a separate limitation from primary-outcome scarcity itself: the lower bound shows the worst-case sqrt(T/B) penalty persists even after the pathwise hard budget is relaxed to an expected acquisition budget.
Post-surrogate timing can change attainable regret
The paper compares acquisition before and after observing the surrogate. For a fixed policy comparison under the same mean acquisition rate, it shows that allowing acquisition to use the surrogate can strictly lower the minimum variance of an unbiased estimate of the primary-outcome value difference.
The stronger result is about rates. On a two-action family where the surrogate does not reveal the better action, a learner that observes the surrogate before deciding whether to acquire can achieve bounded regret, whereas any learner that must decide before seeing the surrogate incurs worst-case regret of order T/B under the same budget. The paper emphasizes that this timing effect holds even though the surrogate does not reveal the optimal action.
This is the paper's sharpest answer to its title question: the ordering of the acquisition decision relative to the surrogate is not a detail, because it can change the attainable regret rate rather than only the constant.
Removing either acquisition factor raises regret
In synthetic experiments, the paper reports that both parts of the acquisition design matter for regret: removing either decision relevance or the post-surrogate residual-RMS refinement increases cumulative regret. The experiments also show that using the current surrogate for acquisition can reduce regret even when it does not reveal the optimal action.
A further synthetic result concerns where residual information sits. The method has lower regret when more residual information lies where represented policies disagree rather than where they agree, even when the overall amount of residual information is fixed. This connects the empirical pattern back to the decision-relevance idea: the same average residual information is more useful when it is concentrated where the policy comparison is unresolved.
The KuaiRec gap widens then narrows with budget
On a KuaiRec benchmark of user-video interactions, the paper builds a contextual acquisition benchmark with K = 5 actions, N = 9 represented policies, and horizon T = 22,417. Each round the learner selects one of five candidate videos, observes a free surrogate defined as whether play duration exceeds 7 seconds, and then decides whether to acquire the primary outcome defined as the watch ratio capped at 1. Both regret and terminal policy value are evaluated using that watch-ratio primary outcome.
The method is compared with a matched relevance-only reference that removes only the learned redistribution after observing the surrogate, so the comparison isolates the contribution of the post-surrogate refinement as the primary-outcome budget varies. Budgets evaluated are 2, 3, 4, 6, 8, 12, 16, and 24 percent.
The paper reports that the regret gap relative to relevance-only acquisition widens and then narrows as the budget grows, with the clearest separation at 4 to 8 percent. At the low end, full-acquisition initialization consumes most of the budget, leaving few later rounds on which post-surrogate refinement can change what is acquired. Toward the high end, both methods observe many more primary outcomes and the contrast narrows.
The paper also distinguishes two evaluation summaries: cumulative regret summarizes the learning trajectory, whereas terminal policy value evaluates the final mixture. The regret contrast remains positive at budgets where the terminal-value contrast is near zero, so learning-path gains need not persist in terminal value.
An opportunity to use the surrogate is not the same as exploiting it
The paper's discussion separates three questions that selective measurement creates. First, selective measurement can bias an uncorrected update, which the augmented feedback addresses without requiring a correct bridge. Second, once that target is protected, the timing question remains: seeing the current surrogate before measurement can leave the minimum comparison variance unchanged in some settings and change the attainable regret rate in others, depending on whether the surrogate distinguishes residual uncertainty on rounds that matter to the policy comparison. Third, the learner does not know in advance which rounds are worth measuring, and the selectively acquired primary outcomes feed both the policy updates and the bridge and residual fits, so evidence collected for action learning also changes which later outcomes are acquired.
The paper also states that its formulation treats measurement as passive: acquiring the current primary outcome reveals it without changing future contexts or outcomes. If measurement itself changes future state, acquisition becomes part of a dynamic decision problem, which is outside the studied setting.
The practical priority that follows from this paper is a comparison, not a general rule. The relevant question is whether the current surrogate can still change which primary outcomes are measured for future learning, and whether the residual uncertainty it leaves is concentrated on rounds where represented policies disagree. The KuaiRec pattern gives the budget context: the separation from relevance-only acquisition is clearest at 4 to 8 percent of primary-outcome budget, weak at the lowest budget because initialization leaves little room for later refinement, and narrow again at the high end where both methods observe many more primary outcomes.
Sources used in this answer
The Surrogate Is Not the Reward: Post-Surrogate Primary-Outcome Acquisition in Contextual Bandits
The Audited Surrogate Bandit sets a pre-surrogate acquisition level from decision relevance and refines it after the surrogate using estimated residual uncertainty, achieving regret of order sqrt(KT log N)(1 + sqrt(T/B)) for a finite class of N policies over K actions while acquiring exactly B primary outcomes over T rounds; on a two-action family where the surrogate does not reveal the better action, post-surrogate acquisition achieves bounded regret while pre-surrogate acquisition incurs worst-case regret of order T/B under the same budget.