{"id":"79f50d80-b76a-434f-8b98-712972d33b8f","arxiv_id":"2507.00851","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"A decision-aware loss and robust uncertainty-set method for learning under endogenous uncertainty, plus a two-stage information-gathering extension, with experiments on pricing, assortment, and power scheduling.","lead":"This paper trains predictive models for decisions that change the outcomes they predict, such as setting a price that changes demand, using a cost-aware loss. It adds a robust variant that hedges against model errors and tests the approach on pricing, inventory, and electricity scheduling.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 2's proof assumes pointwise cost calibration for the population minimizer of squared cost error; for nonlinear costs and restricted function classes this identity fails, so the coverage guarantee is unproven.","rationale":"The reader's weakest assumption identifies a genuine proof error in Theorem 2: the proof treats the population minimizer of the squared cost-error loss as if it were pointwise cost-calibrated (E[c(v,z)|v,x]=c(v,f*(v,x))), which is not implied for nonlinear costs or a restricted function class. This equality is load-bearing because it is used to equate E[V_i(f)] with the squared difference term that drives the martingale concentration bound. Without it, the high-probability coverage guarantee for the uncertainty set is unsupported. I agree with the reader that this is the central correctness risk. I also note a secondary gap: even if the coverage theorem were repaired, the advertised near-optimality of the robust decision would still require an additional argument linking the size of the uncertainty set to the expected-cost suboptimality of the robust action, which the paper does not provide. This does not change the verdict: the paper's main theoretical guarantee is not proven, and the rejection stands. The proposed test recomputes the key identity in a minimal example, which would directly show whether the proof's step is valid.","tokens_in":24643,"tokens_out":10025,"duration_ms":117355,"concrete_test":"Re-derive the proof of Theorem 2 without invoking the calibration identity. In particular, take c(v,z)=z^2, V constant, and F restricted to constant functions. Compute the population minimizer f*, verify whether E[c(v,z)|v,x] equals c(v,f*(v,x)), and check whether E[T_i(f)^2] <= 4 E[V_i(f)] holds for a non-calibrated f*. If the inequality fails, the martingale bound in Eq. (80) collapses and the theorem's proof does not survive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The proof of Theorem 2 (Appendix B) relies on the identity E[c(v_i,z_i)|v_i,x_i] = c(v_i,f*(v_i,x_i)), which the text invokes 'by definition' immediately before Eq. (76)-(78). But f* is defined in Theorem 2 as the population minimizer of E[(c(v,f(x,v))-c(v,z))^2] over F, not as a function satisfying Eq. (2). For nonlinear c and a restricted hypothesis class, the minimizer of squared cost error need not be pointwise cost-calibrated. Consequently E[V_i(f)] is not equal to E[(c(v_i,f)-c(v_i,f*))^2] as claimed in Eq. (78); the cross term involving c(v_i,f*)-E[c(v_i,z_i)|v_i,x_i] can be negative and large enough to break both Eq. (80) and the martingale argument that yields the high-probability coverage bound. The theorem is therefore not established as stated. Even a corrected coverage theorem would only place f* inside U_epsilon; the abstract's additional claim that the robust decision achieves near-optimal expected cost requires a separate bound on E[c(v^R,z)] - min_v E[c(v,z)] in terms of epsilon, which the paper does not supply.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an end-to-end learning framework for stochastic optimization with endogenous uncertainty, in which the learning objective minimizes the squared difference between predicted task costs and observed task costs rather than predicting the uncertain quantity itself. It then introduces a robust variant that constructs an uncertainty set of models with low task loss and makes decisions by minimizing worst-case predicted cost. The authors claim a high-probability guarantee that the true optimal predictor lies in this uncertainty set, and the abstract claims that the robust approach captures near-optimal decisions as a function of data. The paper also extends the framework to a two-stage information-gathering problem and presents computational experiments on pricing, assortment optimization, and electricity scheduling.","tokens_in":24868,"tokens_out":13283,"duration_ms":160482,"significance":"If the theoretical guarantees were valid, the paper would make a useful contribution to decision-focused learning under decision-dependent uncertainty: the problem is well motivated, the task-based loss is a natural alternative to two-stage prediction, and the proposed exact MIQP and sampling algorithms give practical paths to optimization. The extension to information-gathering is novel and the computational study is broad, covering pricing, assortment, and a real-data electricity scheduling problem. However, the central theoretical result, Theorem 2, is not established as stated because the proof relies on an unverified cost-calibration identity, and the abstract's near-optimal-decision claim is not supported by any theorem. These are load-bearing gaps, so the paper is not acceptable in its current form.","major_comments":[{"comment":"The proof of Theorem 2 invokes the identity E[c(v_i,z_i)|v_i,x_i] = c(v_i,f*(v_i,x_i)) 'by definition' (the manuscript writes E[c(v_i,z_i)] = c(v_i,f*(v_i,z_i)) immediately before Eq. (76)). This does not follow from the definition of f* as the population minimizer of the task loss in Eq. (18); it is exactly the cost-calibration property in Eq. (2), which Theorem 2 does not assume and which need not hold when c is nonlinear in z and the hypothesis class F is restricted. Consequently the simplification in Eq. (78) is invalid: E[V_i(f)] is not equal to E[(c(v_i,f)-c(v_i,f*))^2] because the cross term containing c(v_i,f*) - E[c(v_i,z_i)|v_i,x_i] does not vanish. The variance bound in Eq. (74) and the subsequent martingale concentration therefore do not establish the claimed coverage guarantee.","section":"Appendix B, Eqs. (76)-(78); Theorem 2, Eq. (18)"},{"comment":"The statement of Theorem 1 defines the empirical loss \\hat l(f) as a sum over N terms rather than an average, and the additive term is printed as (8 log(2/\\delta)/N)^2 instead of a square-root term. With the sum definition, the right-hand side grows with N and the bound is not the claimed 1/sqrt(N) generalization gap; the proof in Appendix B uses an averaged loss and a square-root term. The theorem statement must be corrected before the generalization result can be evaluated.","section":"Section 2.2, Theorem 1, Eq. (11)"},{"comment":"The uncertainty set U_epsilon in Eq. (13) and the theorem's epsilon_N in Eq. (19) are stated in terms of the summed task loss E(f) from Definition 1, but the proof of Theorem 2 in Appendix B works with the averaged loss \\hat E(f). In addition, the proof concludes with an epsilon of 8 log(|N_gamma|/\\delta)/t + 3M\\gamma and never uses the Delta term that appears in Eq. (19). The statement and proof therefore do not match, and the stated rate for epsilon_N is not derived. The proof also drops the Lipschitz constant L of c in the bound in Eq. (57).","section":"Section 3, Eq. (13); Theorem 2, Eq. (19); Appendix B"},{"comment":"The abstract and the contribution list claim that the robust approach captures near-optimal decisions with high probability, but no theorem in the paper establishes this. Theorem 2 only proves that f* belongs to the uncertainty set U_epsilon; it does not bound E[c(v^R,z)] - min_{v in V} E[c(v,z)] for the robust decision v^R in terms of epsilon or the sample size N. Without such a bound, the headline guarantee that the robust decision is near-optimal is unsupported.","section":"Abstract; Section 1.2; Section 3"}],"minor_comments":[{"comment":"The row for 'Predict then optimize' reports an average difference of 710%, which appears to be a typo (possibly 71.0%); please verify the value.","section":"Table 1"},{"comment":"The proof says one can choose gamma = 1/log N, but this yields a 3M/log N term in epsilon, not the O(M/N) rate claimed in the corollary; choosing gamma of order 1/N would give the stated rate.","section":"Proof of Corollary 1, Appendix B"},{"comment":"The expression 'c(v_i, f*(v_i, z_i))' should read 'c(v_i, f*(v_i, x_i))'.","section":"Eq. (76)"},{"comment":"The text contains the typo 'rboust' in the discussion of Figure 3; it should be 'robust'.","section":"Section 5.1"},{"comment":"The experimental results report point estimates of average cost but no standard errors, confidence intervals, or repeated-seed variability; adding these would strengthen the comparison, particularly for the claims of consistent improvement.","section":"Section 5"}],"recommendation":"reject","confidential_remarks":"The central theoretical guarantee is not established: the proof of Theorem 2 depends on a cost-calibration identity that is not a consequence of the theorem's assumptions, and the near-optimal decision claim in the abstract is not proven by any result in the paper. These are substantive gaps rather than presentation issues. If the authors can repair the proof under a clearly stated assumption and supply the missing decision-suboptimality bound, a substantially revised version might be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate attempt at a hard problem, and the core idea—training on the task loss in the endogenous setting—is worth taking seriously. The main theoretical guarantee in Theorem 2, however, is not proven as stated.\n\nWhat the paper does well: the setup is honest about the absence of counterfactuals. The task-based loss (3) is a natural adaptation of exogenous end-to-end learning, but the adaptation is not trivial: you cannot evaluate decisions you did not take. The robust uncertainty set over models (13) is a sensible construction, and the two-stage information-gathering problem in Section 4 is a genuine extension. The algorithms (MIO, sampling, cutting-plane) are useful, and the experiments cover three distinct problem classes with reasonable baselines. There's no smoke and mirrors in the empirical work; the missing error bars and unreleased code are the main complaints there.\n\nThe soft spot is load-bearing. In the proof of Theorem 2 (Appendix B), the authors use the identity E[c(v_i,z_i)|v_i,x_i] = c(v_i,f*(v_i,x_i)) 'by definition.' But f* is only the population minimizer of squared cost error. For nonlinear cost functions and restricted model classes, the minimizer need not be cost-calibrated. The cross term in Eq. (78) then does not vanish, and the martingale bound leading to coverage can fail. So the high-probability statement that f* lies in U_epsilon is not established in the stated generality. The abstract's stronger claim—that the robust decision achieves near-optimal expected cost—would need a separate argument bounding decision cost in terms of epsilon; the paper only gives containment of f*. This is not a minor typo; it is the central guarantee.\n\nOther issues are minor by comparison: Theorem 1 has a sum/average typo, the choice of epsilon is left to the user, and the experiments lack error bars. None of these would be fatal if the proof were fixed.\n\nWho this is for: researchers in decision-focused learning and contextual optimization. They will find the formulation and the information-gathering extension useful even while the theory is under repair. My advice: send this to a serious referee rather than desk-reject. It deserves a chance to be repaired. If the authors can prove a correct version under stated assumptions—either by assuming a cost-calibrated function lies in F or by softening the theorem—it would be a useful contribution.","headline":"The core task-loss idea is a real contribution, but Theorem 2's proof assumes what it needs to prove, so the paper needs a corrected guarantee before it is publishable.","tokens_in":25421,"tokens_out":1734,"would_cite":false,"duration_ms":21234,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that decision-focused learning under endogenous uncertainty should minimize squared error in decision cost rather than prediction error, and that a robust min-max variant over cost-consistent models yields near-optimal…","keywords":["endogenous uncertainty","decision-focused learning","task-based loss","robust optimization","end-to-end learning","information gathering","pricing","assortment optimization"],"falsifier":"Use a nonlinear cost such as $c(v,z)=z^2$ with bounded $z$ and a hypothesis class too narrow to contain any cost-calibrated predictor; simulate many datasets, compute the population minimizer $f^*$, and record how often $f^*$ actually falls in $U_{\\varepsilon_N}$ at the claimed confidence. If the empirical coverage is below $1-\\delta$, the theorem's coverage claim as stated fails for that setting.","tokens_in":24394,"feed_emoji":"🎯","tokens_out":10137,"duration_ms":110396,"temperature":0.7,"pith_summary":"Decisions often change the very quantities a model must predict: prices alter demand, stock levels alter sales, and you only ever observe the outcome of the action you actually took. This paper claims that the right training objective in such settings is a task-based loss, the squared difference between the cost of a historical decision under the model's forecast and the cost that was actually observed. On top of that loss, the paper builds an uncertainty set of all models whose task-based error on the data is small, and chooses decisions that maximize the worst-case predicted cost over that set; it proves this robust decision is near-optimal in expected cost with high probability and that the needed uncertainty radius shrinks as data grows. If these claims hold, they give a practical, principled replacement for counterfactual information in pricing, assortment, and other decision-focused learning problems.","feed_headline":"When prices change demand, train on cost, not forecasts","feed_subtitle":"Worst-case sets of cost-consistent models deliver near-optimal decisions as data grows.","key_machinery":"The load-bearing object is the cost-calibrated forecast: a function $f^*$ for which $c(v,f^*(x,v))=\\mathbb{E}[c(v,z)\\mid v,x]$, so that plugging a point forecast into the cost function reproduces expected cost. Training uses the task-based loss $E(f)$ as an empirical surrogate for this identity, and robustness is carried by the uncertainty set $U_\\varepsilon=\\{f\\in F: E(f)\\le \\beta+\\varepsilon\\}$, from which the decision rule $v^*_{\\mathrm{robust}}=\\arg\\min_v \\max_{f\\in U_\\varepsilon} c(v,f(x,v))$ is formed. The theoretical arguments combine Rademacher complexity bounds for the generalization gap with covering numbers, Lipschitz continuity of the models in their parameters, and a martingale concentration inequality for the robust coverage guarantee. Computationally, the paper contributes an exact mixed-integer reformulation when costs are piecewise-linear convex, a sampling-based training heuristic, and a cutting-plane algorithm for the outer minimax problem.","core_discovery":"The central claim is that aligning learning with downstream decisions under endogenous uncertainty reduces to minimizing $E(f)=\\sum_n (c(v_n,f(x_n,v_n))-c(v_n,z_n))^2$, and that this objective is the correct substitute for the unavailable counterfactual data. The paper shows under a cost-calibration condition, $c(v,f^*(x,v))=\\mathbb{E}[c(v,z)\\mid v,x]$, the forecast $f^*$ induces optimal decisions. Its robust theorem then states that for the uncertainty set $U_\\varepsilon=\\{f\\in F: E(f)\\le \\beta+\\varepsilon\\}$ with $\\varepsilon$ chosen according to covering numbers and Lipschitz constants, the best-in-class predictor lies in $U_\\varepsilon$ with probability $1-\\delta$, so the min-max rule $v^*_{\\mathrm{robust}}=\\arg\\min_v \\max_{f\\in U_\\varepsilon} c(v,f(x,v))$ attains near-optimal expected cost; for linear classes $\\varepsilon=O((d\\log N+\\log 1/\\delta)/N)$. The paper also extends the framework to two-stage information-gathering problems, where the first decision is which random variable to observe before a second-stage forecast and decision.","pith_inferences":["Because robustness is defined over models rather than over outcome realizations, the uncertainty set can be composed with exogenous end-to-end losses for mixed problems, not just the polling example in the paper.","The cost-calibration diagnosis suggests a testable extension: augment the uncertainty-set radius with an approximation-error term when no function in the class is exactly cost-calibrated, and re-check the coverage guarantee.","The information-gathering formulation generalizes to active feature acquisition in supervised learning, where the first-stage choice is which covariate to buy information about before the forecast and decision.","The assortment finding that the optimal predictor can be a quantile of demand hints that task-based losses may automatically learn risk-averse statistics for nonlinear costs, which could be tested on other cost functions."],"forward_implications":["Under endogenous uncertainty, the task-based loss replaces unobservable counterfactuals with observed decision costs, so no action-outcome pairs beyond history are needed to train a decision-aware model.","The robust uncertainty set contains the true best-in-class predictor with probability at least $1-\\delta$, and its radius shrinks as $O((d\\log N+\\log 1/\\delta)/N)$ for linear models, so protection against model error becomes cheaper with more data.","Decisions obtained by the min-max rule inherit near-optimal expected cost with high probability, which is the property a planner needs before deploying learned forecasts in pricing or inventory.","The same end-to-end machinery applies to two-stage information-gathering problems, where the first decision selects which random variable to observe and the second decision is made from the updated forecast.","On the paper's pricing, assortment, and electricity-scheduling experiments, the approach consistently beats two-stage prediction, direct reward learning, and robust offline baselines in achieved cost."],"supporting_citations":[{"why":"Supplies the Rademacher complexity bounds and the vector contraction inequality used in Theorem 1.","marker":"Bartlett and Mendelson (2002)"},{"why":"Provides the task-based end-to-end training idea and the electricity scheduling setup reused in the information-gathering experiments.","marker":"Donti et al. (2017)"},{"why":"Defines the exogenous predict-then-optimize benchmark whose decision-aware objective the endogenous loss is designed to replace without counterfactuals.","marker":"Elmachtoub and Grigas (2022)"},{"why":"Gives the cutting-plane scheme whose convergence the outer robust optimization algorithm relies on.","marker":"Kelley (1960)"},{"why":"Presents a regularized pessimistic inner-problem approach that the paper contrasts with its alternating projection Algorithm 2.","marker":"Xie et al. (2021)"},{"why":"Represents the conservative offline reinforcement learning baseline compared in the computational experiments.","marker":"Kumar et al. (2020)"}],"fun_headline_variants":["Train on cost, not forecasts, for endogenous decisions","Cost-consistent robust ML captures near-optimal decisions","Align learning with downstream decisions under uncertainty","End-to-end framework for decision-aware ML"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The robust guarantee assumes the best model inside the chosen class is exactly cost-calibrated, meaning its predicted cost equals the true conditional expected cost at every action, and for nonlinear cost functions, being the minimizer of squared cost error does not by itself force that property.","fun_headline_variants_meta":{"raw":{"variants":["Train on cost, not forecasts, for endogenous decisions","Cost-consistent robust ML captures near-optimal decisions","Align learning with downstream decisions under uncertainty","End-to-end framework for decision-aware ML"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000204,"raw_usage":{"total_tokens":1449,"prompt_tokens":1063,"completion_tokens":386,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":679,"completion_tokens_details":{"reasoning_tokens":328}},"tokens_in":679,"tokens_out":386,"duration_ms":4923,"temperature":1.0,"reasoning_tokens":328,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:07:39.357807+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Use a nonlinear cost such as $c(v,z)=z^2$ with bounded $z$ and a hypothesis class too narrow to contain any cost-calibrated predictor; simulate many datasets, compute the population minimizer $f^*$, and record how often $f^*$ actually falls in $U_{\\varepsilon_N}$ at the claimed confidence. If the empirical coverage is below $1-\\delta$, the theorem's coverage claim as stated fails for that setting.","supporting_citations":[{"cited_title":"Advances in neural information processing systems 30","cited_arxiv_id":null,"evidence_quote":"Provides the task-based end-to-end training idea and the electricity scheduling setup reused in the information-gathering experiments."},{"cited_title":"Journal of the society for Industrial and Applied Mathematics 8(4):703--712","cited_arxiv_id":null,"evidence_quote":"Gives the cutting-plane scheme whose convergence the outer robust optimization algorithm relies on."},{"cited_title":"Advances in neural information processing systems 34:6683--6694","cited_arxiv_id":null,"evidence_quote":"Presents a regularized pessimistic inner-problem approach that the paper contrasts with its alternating projection Algorithm 2."},{"cited_title":"Advances in Neural Information Processing Systems 33:1179--1191","cited_arxiv_id":null,"evidence_quote":"Represents the conservative offline reinforcement learning baseline compared in the computational experiments."}],"review_version":1}