{"id":"f2429ddb-089a-424e-a13b-a889d32717fd","arxiv_id":"2506.19155","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A Wasserstein-regularized framework computes relative counterfactual explanations for facility location with binary decisions and endogenous uncertainty.","lead":"This paper proposes a method to compute counterfactual explanations for facility-location decisions, finding the smallest context changes that make an alternative plan acceptable. Planners can ask what would need to change, such as a site's attractiveness, before a rejected location would be included.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 1 contains an impossible runtime row, so the headline efficiency claim is not currently supported; the advertised Montreal case study is also absent.","rationale":"The reader's stated weakest assumption is the known-distribution assumption, which the paper acknowledges in Section 1. That is a genuine limitation but it is scoped and does not directly bear on the optimization methodology. The reader's rationale, however, also flags the internally inconsistent runtime table and the missing advertised case study, which are the concerns I regard as most load-bearing: they affect the paper's central empirical claims of computational efficiency and real-world validation. My recommendation is therefore to keep the CONDITIONAL verdict: the methodological contribution is plausible and the formulation appears coherent, but the empirical evidence must be corrected and completed before the headline claims can be accepted. I mark agreement as 'partial' because the reader's explicit weakest-assumption field and my primary concern differ, even though the overall verdict and required fixes align.","tokens_in":13839,"tokens_out":17668,"duration_ms":177781,"concrete_test":"Run the public repository code for the N=100, D=10, r=8, λ=0.1 configuration with the stated 3,600-second limit and ten random seeds, and recompute the average time, median time, TL count, and gap. If the corrected row still shows a decisive speedup relative to the λ=0 row, the efficiency claim survives; if the row cannot be reproduced or the speedup disappears, the abstract's runtime claim must be revised. Separately, search the manuscript and repository for the Montreal EV-charging case study to determine whether the advertised validation exists anywhere.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central advertised contribution includes the claim that the Wasserstein regularization 'leads to a reduction in computation times compared to its unregularized counterpart' and yields sparser counterfactuals. This claim rests on Table 1, but that table is internally inconsistent. For the configuration N=100, D=10, r=8, λ=0.1, the table reports TL=5 (five of ten instances hit the 3600-second time limit) while the average time is 1,094 seconds. Since a time-limited run must have elapsed 3,600 seconds, five such runs alone force the average to be at least 1,800 seconds. The reported average is therefore impossible as stated. A similar inconsistency does not appear in every row, but one impossible row is enough to invalidate the table as reported evidence. Additionally, the abstract supplied with the paper advertises a real-world case study on electric vehicle charging station planning in Montreal, but the full text contains no such case study, no corresponding section, and no experimental results for it. The abstract therefore overstates the validation actually performed. These two issues directly undermine the empirical pillar of the central claim: the claim of computational efficiency is supported by an internally inconsistent table, and the claim of real-world validation is unsupported by the manuscript body. The known-distribution assumption is a real limitation, but it is explicitly scoped in Section 1 and does not by itself invalidate the optimization formulation; the data-quality problems are more immediately load-bearing for the paper's headline assertions.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies relative counterfactual explanations for contextual stochastic optimization problems in which the outcome distribution depends on both the context and the decisions. It formulates the explanation task as a non-convex optimization problem (2), introduces a cost that combines ℓ1 dissimilarity in a transformed feature space with a 2-Wasserstein regularization term (4), and proposes a model-free lower bound plus a greedy warm start. The method is specialized to a choice-based competitive facility location problem under a multinomial logit model; after a Haase-type reformulation, explanations are computed by solving the mixed-integer bilinear program (9). Section 5 reports experiments on a small illustrative instance and on synthetic instances of varying size, claiming that moderate Wasserstein regularization reduces computation time and yields sparser counterfactuals. The supplied abstract also claims validation on a real-world electric vehicle charging station planning case study in Montreal, but this case study is not present in the manuscript body.","tokens_in":14172,"tokens_out":12133,"duration_ms":123491,"significance":"If the computational claims held, this would be a useful contribution: it extends relative counterfactual explanations from continuous expert-provided target solutions to problems with binary decisions and endogenous uncertainty, and it allows a desired feasible set rather than a single target solution. The mathematical derivation from the MNL model to formulation (9) follows Haase (2009) and is internally consistent, and the authors make code and instances publicly available, which supports reproducibility. The lower-bound and warm-start scheme is a sensible practical addition. The significance of the empirical claims is, however, currently undermined by an arithmetically impossible row in Table 1 and by an abstract that advertises a real-world validation absent from the body; the modeling contribution itself appears sound.","major_comments":[{"comment":"The row for N=100, D=10, r=8, λ=0.1 reports TL=5 and average time 1,094.136 s. Since five runs hit the 3,600 s time limit, any valid average over the ten instances must be at least 1,800 s, so the reported average is arithmetically impossible. This row directly supports the paper's headline claim that λ=0.1 reduces computation time, and the table as reported therefore does not support that claim. Please correct the data, recalculate the summary statistics, or rerun the affected instances before the efficiency claim can be accepted.","section":"Section 5, Table 1"},{"comment":"The abstract supplied with the paper states that the framework is validated on a real-world case study of electric vehicle charging station planning in Montreal. The full text contains no such case study: Section 5 contains only the illustrative example and the synthetic instances of Tables 1–2, and Section 6 does not mention Montreal. Either the case study and its results must be added to the manuscript, or the abstract's validation claim must be removed or corrected.","section":"Abstract; Section 5"},{"comment":"The statement that Wasserstein regularization yields sparser counterfactuals is stronger than what the table shows. For N=200, D=20, r=8, sparsity increases from 0.075 at λ=0 to 0.105 at λ=0.1 and 0.205 at λ=1, and several λ=1 rows, such as N=100, D=10, r=8, are less sparse than the corresponding λ=0 row. The qualitative claim in the text should be qualified as instance-dependent, or the analysis should explain when and why the sparsity improvement holds.","section":"Section 5, Table 1"}],"minor_comments":[{"comment":"The symbol D is used both for the set of candidate locations and for the desired feasible space; constraint (8g), written as \"zd∈D\", appears to be a typo for \"z∈D\" (or \"z∈\\mathcal{D}\"), and the notation should be disambiguated.","section":"Section 4.1"},{"comment":"In the warm-start description, Step 2 says to calculate the factual captured demand \"for each facility d,\" but the displayed quantity Q_factual = ∑_n q_n ∑_d P0_n(d) is a single total over all facilities; please clarify the wording.","section":"Section 4.2"},{"comment":"The phrase \"the Wasserstein term is scaled by its bound\" is not defined; please specify the exact scaling factor used in the objective before reporting the experiments.","section":"Section 5"},{"comment":"The constraint ranges \"d∈D e∈E n∈N\" appear to include e∈E unintentionally in (9g), which does not depend on e; this should be corrected for readability.","section":"Equations (9g)–(9i)"},{"comment":"The captions contain typos: \"solid dimonds\" should be \"solid diamonds\" in Figure 1, and \"a a solution\" should be \"a solution\" in Figure 2.","section":"Figures 1 and 2"}],"recommendation":"major_revision","confidential_remarks":"The main issues are empirical rather than methodological: the impossible runtime row in Table 1 and the mismatch between the abstract's Montreal case-study claim and the manuscript body suggest a versioning or reporting error. If these are corrected, the paper is likely viable. I found no reason to doubt the internal consistency of the MNL-to-bilinear derivation or the modeling contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful part of this paper is the formulation. Ramírez-Ayerbe and Frejinger take relative counterfactual explanations, previously defined for LPs and for data-driven optimization without binary decisions, and extend them to contextual stochastic problems with binary decision variables and endogenous uncertainty. Generalizing the target from a single expert solution to a desired set D is a real step, and the mixed-integer bilinear reformulation built on Haase's MNL linearization looks internally consistent. The model-free lower bound and greedy warm start are sensible engineering. The code and instances are public, which makes the numerical work independently checkable. The paper also states its main limitation up front: P(y|z,x) is assumed known. That is a real limitation, but it is scoped and does not invalidate the optimization contribution.\n\nThe soft spots are in the experiments, and they are concrete. Table 1 contains an arithmetically impossible row: for N=100, D=10, r=8, λ=0.1, five out of ten instances hit the 3600-second limit, yet the average reported time is 1094 seconds. Those five runs alone force an average of at least 1800 seconds. This is not a rounding issue; the row as printed cannot be correct. Since the abstract's efficiency claim ('leads to a reduction in computation times') rests largely on this table, that claim is currently unsupported. Some other rows do show regularized solving faster, but the inconsistency plus the high number of timeouts and large optimality gaps in the larger instances mean the scalability evidence is weaker than the prose suggests. Second, the abstract advertises a real-world case study on EV charging station planning in Montreal. The full text has no such case study, no corresponding section, no results. I double-checked the full text; it is not there. The abstract overstates what the paper validates.\n\nThere is also a smaller point on sparsity: the claim that Wasserstein regularization yields sparser counterfactuals is asserted from Table 1's ℓ0-based sparsity column, but with timeouts and the data problems, that comparison is also shaky.\n\nWho is this for? Anyone working on explainable optimization, counterfactual explanations, or choice-based facility location. The methodological content deserves a serious referee; the experiments need to be redone and the abstract aligned with what is actually in the paper. I would not desk-reject this, but I would send it back with the expectation that Table 1 is fixed, the Montreal case study is either added or removed from the abstract, and the empirical claims are scaled to what the data actually support.","headline":"Solid formulation contribution, but an impossible runtime row and a missing advertised case study undercut the empirical headline; worth a serious referee after rework.","tokens_in":14676,"tokens_out":2563,"would_cite":false,"duration_ms":24317,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90B80","90C11","90C15","90C26"],"pacs":[],"model":"deepseek-v4-flash","headline":"A Wasserstein-regularized mixed-integer bilinear program computes relative counterfactual explanations for binary-decision contextual stochastic programs with endogenous uncertainty, demonstrated on competitive facility location.","keywords":["counterfactual explanations","contextual stochastic optimization","endogenous uncertainty","competitive facility location","multinomial logit model","Wasserstein distance","mixed-integer bilinear programming","explainable optimization"],"falsifier":"Run the instance families of Table 1 with identical warm starts and a one-hour limit for $\\lambda=0$ and $\\lambda=0.1$: if the unregularized model reaches optimality in less time on a majority of the larger instances, the claimed computational benefit of Wasserstein regularization is not general. A sharper test is to take instances where the factual choice distribution is nearly uniform, where the Wasserstein penalty should force the largest distortions and the unregularized objective should look relatively cheap; if $\\lambda=0.1$ still dominates there, the speedup is robust to distribution shape.","tokens_in":13672,"feed_emoji":"📍","tokens_out":10432,"duration_ms":100475,"temperature":0.7,"pith_summary":"Relative counterfactual explanations answer the question: what is the smallest change in the context that would make a desired decision acceptable? The paper claims these explanations can be computed for contextual stochastic optimization problems whose uncertainty is endogenous—the decision itself changes the distribution of the random outcome—even when the decision variables are binary, a setting it says earlier relative-explanation work did not cover. It makes the computation practical for a choice-based competitive facility location problem by minimizing an $\\ell_1$ cost on transformed attractiveness covariates plus a 2-Wasserstein penalty that keeps the counterfactual demand distribution close to the factual one, and by reformulating the result as a mixed-integer bilinear program. If the claims hold, planners can learn, for example, which attractiveness improvements or environmental changes would justify opening a charging station that the current solution excludes, while limiting expected demand loss to a chosen factor $\\alpha$.","feed_headline":"Wasserstein penalty makes counterfactual siting faster and sparser","feed_subtitle":"Their method keeps demand within a chosen factor while finding the fewest context changes that open a desired site.","key_machinery":"The load-bearing object is the relative counterfactual explanation: a new context $x$ for which some feasible decision $z\\in\\mathcal{D}$ earns a factor $\\alpha$ of the factual expected reward. The argument runs through the standard mixed-integer linear reformulation of multinomial logit choice probabilities, extended so that the transformed attractiveness values $\\phi_d(x)=\\exp(\\bar{v}_d(x_d))$ are decision variables rather than fixed parameters; this produces bilinear constraints linking the opening decisions, the attractiveness values, and the choice probabilities. The Wasserstein regularization enters as a finite optimal transport problem: with $\\pi^n$ coupling the factual and counterfactual choice distributions, the objective contains $\\lambda\\sum_n\\sum_{c,c'}\\pi^n_{cc'}\\delta(c,c')^2$. A model-free version that optimizes directly over probabilities gives a lower bound, and a greedy feasibility heuristic supplies the warm start that makes the bilinear program solvable within the hour limit on the test instances.","core_discovery":"The paper's central claim is that including the squared 2-Wasserstein distance between the factual and counterfactual choice distributions in the objective is not just a way to make counterfactuals realistic; it also accelerates solving the explanation problem and produces sparser solutions. In the multinomial logit facility location model, the explanation problem with a desired facility set is formulated as a single mixed-integer bilinear program over attractiveness variables $\\phi_d(x)$, opening variables $z_d$, and optimal transport plans $\\pi^n$, where the Wasserstein term is the transport cost between the factual and counterfactual choice distributions. A model-free relaxation over probability distributions provides a lower bound, and a constructive greedy heuristic provides a feasible warm start. On randomly generated instances, the regularized version with $\\lambda=0.1$ reaches the one-hour time limit less often and yields sparser solutions than the unregularized version, while keeping the counterfactual choice probabilities close to the factual ones.","pith_inferences":["I infer that the Wasserstein penalty will matter most when the factual choice probabilities are concentrated: with sharply peaked distributions the transport cost forces probability mass to move along short paths, whereas the unregularized $\\ell_1$ objective can jump to an arbitrary distribution at the same covariate cost; the paper's experiments do not vary the concentration of the factual distri","A natural extension the paper leaves open is to estimate $P(y\\mid z,x)$ from data and propagate estimation error into the explanations; I would expect the slack in the demand constraint to be a useful diagnostic for when a found counterfactual is an artifact of a misspecified model.","I infer from the reported instances that the speedup from regularization is most reliable for small budgets: several $r=8$ instances still reach the time limit even with $\\lambda=0.1$, so the computational benefit may weaken as the budget grows."],"forward_implications":["For any desired facility configuration, planners get a concrete, minimal context shift that makes that configuration acceptable, expressed in the same attractiveness or environmental variables the demand model uses.","The same mixed-integer bilinear template transfers to other binary-decision problems with endogenous uncertainty—network design, assortment planning, school siting—as long as the outcome distribution is known and depends on covariates through a monotone transformation.","The model-free lower bound gives a certificate of how much structural realism costs: if the bound is far below the model-based value, no context can realize the cheap distributional shift the bound finds.","Regularized explanations are sparser and produce smoother demand transitions, so they are more likely to be perceived as plausible by stakeholders than explanations that change many small features.","Because the desired space $\\mathcal{D}$ can be any subset of configurations, the same code can answer what would make any one of a family of alternatives acceptable, not just a single expert-chosen target."],"supporting_citations":[{"why":"Supplies Definition 1.1, the notion of relative counterfactual explanation that the paper adopts and extends to binary decisions and endogenous uncertainty.","marker":"Kurtz et al. (2025)"},{"why":"Introduced relative explanations in data-driven optimization; the paper generalizes their expert-target setting to a desired feasible set.","marker":"Forel et al. (2023)"},{"why":"Previous contextual counterfactual framework with epsilon-explanations; the paper contrasts its desired-space formulation and inherits its continuous-covariate restriction.","marker":"Vivier-Ardisson et al. (2024)"},{"why":"Provides the mixed-integer linear reformulation of multinomial logit choice probabilities that the paper extends to variable attractiveness covariates.","marker":"Haase (2009)"},{"why":"Background for the squared 2-Wasserstein distance and its finite-dimensional optimal-transport formulation used as the regularizer.","marker":"Peyré et al. (2019)"},{"why":"Survey that frames contextual stochastic optimization and the known-distribution assumption the paper adopts.","marker":"Sadana et al. (2025)"},{"why":"Supplies the notation and demand-capture formulation for choice-based competitive facility location used in the application.","marker":"Legault and Frejinger (2025)"}],"fun_headline_variants":["Wasserstein term yields sparser, faster counterfactuals for facility siting","Sparse counterfactuals for facility location via Wasserstein regularization","EV charging site justification: sparser counterfactuals via Wasserstein penalty","For competitive facility location, Wasserstein term gives sparse explanations","Sparse, explainable counterfactuals for contextual stochastic siting"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework assumes the conditional distribution $P(y\\mid z,x)$ is known, and every explanation is relative to that fixed model; if the model is misspecified, the computed counterfactual changes are not reliable evidence about what would happen in the world.","fun_headline_variants_meta":{"raw":{"variants":["Wasserstein term yields sparser, faster counterfactuals for facility siting","Sparse counterfactuals for facility location via Wasserstein regularization","EV charging site justification: sparser counterfactuals via Wasserstein penalty","For competitive facility location, Wasserstein term gives sparse explanations","Sparse, explainable counterfactuals for contextual stochastic siting"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000412,"raw_usage":{"total_tokens":2154,"prompt_tokens":992,"completion_tokens":1162,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":1070}},"tokens_in":608,"tokens_out":1162,"duration_ms":9752,"temperature":1.0,"reasoning_tokens":1070,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:35:47.694530+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the instance families of Table 1 with identical warm starts and a one-hour limit for $\\lambda=0$ and $\\lambda=0.1$: if the unregularized model reaches optimality in less time on a majority of the larger instances, the claimed computational benefit of Wasserstein regularization is not general. A sharper test is to take instances where the factual choice distribution is nearly uniform, where the Wasserstein penalty should force the largest distortions and the unregularized objective should look relatively cheap; if $\\lambda=0.1$ still dominates there, the speedup is robust to distribution shape.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced relative explanations in data-driven optimization; the paper generalizes their expert-target setting to a desired feasible set."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Previous contextual counterfactual framework with epsilon-explanations; the paper contrasts its desired-space formulation and inherits its continuous-covariate restriction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the mixed-integer linear reformulation of multinomial logit choice probabilities that the paper extends to variable attractiveness covariates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Survey that frames contextual stochastic optimization and the known-distribution assumption the paper adopts."}],"review_version":1}