{"id":"774c9a54-0693-4dca-a446-9a8a780b1ef2","arxiv_id":"2505.17379","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"OIAFC and OIAFB identify an (epsilon, delta)-optimal scoring rule in online principal-agent information acquisition with instance-dependent sample complexity, but the proven rate differs from the advertised rate.","lead":"This paper gives two algorithms, OIAFC and OIAFB, for identifying a near-optimal scoring rule in an online principal-agent information acquisition problem, with sample-complexity bounds for both fixed-confidence and fixed-budget settings. The authors claim the first instance-dependent sample-complexity guarantee for this problem, improving on Chen et al. (2023).","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The advertised instance-dependent bound does not follow from Theorem 1: the oracle-margin factor ε^{-2}B_S^2 M survives in every forced-exploration bound, so the headline O~(MΣΔ_k^{-2}+ε^{-2}) is unsupported; the weaker theorem is the actual proven contribution.","rationale":"The reader's weakest-assumption analysis and my stress-test converge on the same load-bearing point: the action-informed oracle margin ε enters the forced-exploration analysis and the final complexity, and this is precisely what makes the proven bound weaker than the advertised one. I am not claiming Theorem 1 is false; the proof appendix contains a substantial attempt and the oracle assumption is inherited from Chen et al. (2023), where a hard instance shows some such oracle is necessary. The concern is that the central advertised contribution, the instance-dependent bound of the MAB form O~(MΣΔ_k^{-2}+ε^{-2}), is not what the theorem proves. The extra ε^{-2}B_S^2 M factor is not a cosmetic presentation issue because it changes the qualitative dependence on the oracle and on the target accuracy. The OIAFB line-13 inversion is a separate but telling defect: it means the fixed-budget algorithm as printed does not perform the forced exploration the analysis counts. Together these issues fully justify the reader's CONDITIONAL verdict: the paper can likely be repaired by restating the main theorem, correcting the pseudocode, and removing the unsupported near-optimality remarks, but as written the headline result is unproven. I therefore keep the verdict unchanged rather than escalating to rejection, because the underlying algorithmic ideas and the corrected theorem may still constitute a valid contribution.","tokens_in":30687,"tokens_out":9401,"duration_ms":79709,"concrete_test":"Symbolically recompute the bound in Section F.4 without dropping the oracle margin: substitute H_Δ = 4(B_S+B_u)^2(ε_target^{-2}+Σ_{k≠k*}Δ_k^{-2}) into the τ_2 bound from Lemma 4 and collect powers of ε_oracle^{-1}. If the resulting closed form contains a separate ε_oracle^{-2}B_S^2 M ε_target^{-2} term (or ε_oracle^{-2}B_S^2 M ΣΔ_k^{-2}), then the introduction's advertised O~(MΣΔ_k^{-2}+ε^{-2}) bound is not derivable from Theorem 1, and the paper must be revised to state only the weaker bound. This is a direct algebra check and requires no new simulation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The introduction advertises an instance-dependent sample complexity of O~(M(Σ_{k≠k*}Δ_k^{-2}) + ε^{-2}) for OIAFC, but Theorem 1 proves τ = O~(ε^{-2}B_S^2 M H_Δ), where ε is the action-informed oracle margin from Assumption 1 and H_Δ already contains the target-accuracy term ε^{-2}. Thus the proven bound contains an extra ε^{-2}B_S^2 M factor that is not present in the advertised bound. This factor is not a harmless constant: Assumption 1 only asserts existence of a positive margin ε, and the proof of Lemma 4 carries ε^{-1} into the count of forced explorations. No step in Section F or G bounds ε away from zero or cancels it. Consequently, the only instance-dependent guarantee actually derived is O~(ε^{-2}B_S^2 M(ε^{-2}+ΣΔ_k^{-2})), which is weaker than advertised and does not support the claim in Remark 4 that the result aligns with MAB instance-dependent bounds. This is a load-bearing gap because the paper's central novelty is precisely the advertised instance-dependent bound. The OIAFB pseudocode in Algorithm 2 line 13 also triggers binary search when k_t = k*_t and skips it when k_t ≠ k*_t, the opposite of the rule used in the analysis, so the fixed-budget theorem does not apply to the printed algorithm. These are concrete, fixable issues, but the headline claim is currently unproven.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies best scoring rule identification (BSRI) in an online principal-agent information acquisition model. It proposes OIAFC for fixed-confidence identification and OIAFB for fixed-budget identification, both based on estimated belief distributions and pairwise cost differences, an optimism-based linear program (UCB-LP), a conservative sampling rule that mixes an action-informed oracle rule with the current LP solution, and a binary-search forced-exploration procedure. The authors claim an instance-dependent fixed-confidence bound O~(M(sum_{k≠k*} Δ_k^{-2}) + ε^{-2}), an instance-independent bound O~(M K ε^{-2}), and a matching fixed-budget result, improving on the instance-independent bound of Chen et al. (2023).","tokens_in":30887,"tokens_out":6444,"duration_ms":51242,"significance":"If the advertised bounds were proven, the paper would give the first instance-dependent fixed-confidence upper bound and the first fixed-budget analysis for BSRI, a natural pure-exploration variant of the online principal-agent information acquisition problem. The algorithmic machinery is nontrivial: the UCB-LP formulation, the time-varying trade-off parameter α_t^k, the stopping rule, and the binary-search analysis are all concrete and, in the instance-independent parts, the proof strategy is coherent. The paper also usefully identifies the role of the action-informed oracle margin in forced exploration. However, the central instance-dependent claim is not supported by the stated theorem, and the fixed-budget pseudocode is inconsistent with its analysis, so the main novelty is currently unproven as presented.","major_comments":[{"comment":"The introduction (first contribution bullet) advertises an instance-dependent sample complexity of O~(M(Σ_{k≠k*} Δ_k^{-2}) + ε^{-2}) for OIAFC, and Remark 4 claims that the result aligns with standard MAB instance-dependent bounds. Theorem 1 instead proves τ = O~(ε^{-2} B_S^2 M H_Δ), where H_Δ = 4(B_S+B_u)^2(ε^{-2}+Σ_{k≠k*} Δ_k^{-2}) by Definition 3. Even after suppressing logarithmic factors, the proven bound is O~(ε^{-2}B_S^2M(ε^{-2}+ΣΔ_k^{-2})), which contains an extra multiplicative ε^{-2}B_S^2M factor absent from the advertised bound. Assumption 1 only asserts that a positive oracle margin ε exists; Lemma 4 carries ε^{-1} into the forced-exploration count, and Lemma 12 does the same in the definition of N*_k. No step in Sections F or G lower-bounds ε or cancels its dependence. This is load-bearing because the paper's headline novelty is precisely the instance-dependent rate, so either the advertised bound must be proven or the claims and Remark 4 must be revised to the weaker theorem.","section":"Section 1 and Theorem 1"},{"comment":"Algorithm 2 (OIAFB) executes the binary search when k_t = k*_t (lines 12–14), which is the reverse of OIAFC's rule in Algorithm 1, line 12, where the binary search is executed when k_t ≠ k*_t. The text in Section 5.2 states that OIAFB shares the same sampling rule and forced-exploration strategy as OIAFC, and the fixed-budget analysis (Lemma 14 and Theorem 2) counts binary searches only on rounds in which the agent deviates from the desired arm. The theorem therefore does not apply to Algorithm 2 as printed: under the printed condition, the algorithm never performs forced exploration on the deviating rounds that the analysis relies on. The condition should be reversed, or the analysis and text should be changed to match the pseudocode.","section":"Appendix D.1, Algorithm 2"},{"comment":"The proof of Lemma 4 decomposes τ_2 using indicators of the form 1{BS=1, Γ^{t0(t)}(k0(t),k1(t)) ≤ α^{t0(t)}_{k0(t)}} and 1{BS=1, Γ^{t0(t)}(...) > α^{t0(t)}_{k0(t)}}. The manuscript does not state a normalization or loss-of-generality assumption that would justify setting BS=1. Since every confidence radius, every UCB-LP constraint, and the definition of Γ scale with BS, this is not a harmless notational convenience. The proof should either state the normalization explicitly and show how the general case follows, or remove the condition. As written, the forced-exploration bound in Lemma 4 is not fully established for general BS.","section":"Section F.2, proof of Lemma 4"}],"minor_comments":[{"comment":"The paper uses ε both for the target accuracy ǫ in Definition 2 and for the oracle margin ε in Assumption 1, despite the notation table distinguishing the two. This ambiguity is especially confusing in Theorem 1, Lemma 4, and Definition 3, and it contributes to the mismatch identified above. Please disambiguate consistently.","section":"Notation throughout"},{"comment":"The printed sampling rule contains the expression `αt_{k*}^k`, which appears to be a typo for α_t^{k*_t} as defined in the surrounding text.","section":"Algorithm 1, line 10"},{"comment":"The budget formula in Corollary 2 contains the term max(B_S^2 ε^{-2}, 1), while the prose says the budget is O~(ε^{-2}B_S^2 M H_ǫ). These statements should be reconciled, since when B_S^2 ε^{-2} < 1 the printed formula does not contain the ε^{-2}B_S^2 factor.","section":"Corollary 2"},{"comment":"In the paragraph following Algorithm 3, the text refers to k*(S2), although the algorithm signature names the two inputs k*(S0) and k*(S1). This appears to be a typo.","section":"Appendix D.2, Algorithm 3 discussion"},{"comment":"There are several typographical errors in the text, including 'involes', 'incurrs', and 'principal' for 'principle' in the introduction; these do not affect the technical content but should be corrected in revision.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript contains a genuine algorithmic contribution, and the instance-independent analysis appears plausible, but the advertised instance-dependent rate is not what Theorem 1 proves, and the OIAFB pseudocode is inconsistent with its own analysis. The first issue is substantive and load-bearing: if the stronger bound cannot be proven, the paper should be reframed around the weaker theorem and Remark 4 should be removed or qualified. The second issue is a one-line fix but is essential for correctness. No concerns about attribution or scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper has a real new result, but the introduction sells a bound the theorems do not prove. The bullet claims O~(MΣΔ_k^{-2}+ϵ^{-2}) for OIAFC; Theorem 1 actually gives O~(ε^{-2}B_S^2 M H_Δ), with H_Δ containing ϵ^{-2}+ΣΔ_k^{-2}. The extra oracle-margin factor ε^{-2}B_S^2 is not a typo: it comes from Lemma 4 and survives to the end. The conclusion states the weaker bound honestly, so the main fix is to align Section 1 and Remark 4.\n\nThe second issue is Algorithm 2 (OIAFB) in Appendix D.1: line 13 runs the binary search when k_t = k*_t, the opposite of the condition used in the analysis and in OIAFC. As printed, the fixed-budget theorem does not apply to the algorithm. That is likely a transcription error, but it has to be fixed.\n\nWhat is genuinely new: this is the first instance-dependent sample-complexity upper bound for best scoring rule identification in the online principal-agent setting, and the instance-independent guarantee in Corollary 1 improves on Chen et al. (2023) by a large margin (roughly O~(B_S^2ε^{-2}MKϵ^{-2}) vs O~(K^6C_O^3ϵ^{-6})). The adaptive α_t^k and the β_t stopping rule are sensible, and the appendix contains real proof effort with few gaps. The dependence on the action-informed oracle margin is inherited from the model (Chen et al. use the same oracle), so the issue is not that the bound has an ε factor; it is that the paper's own headline ignores it.\n\nThe math is mostly sound. I did not find circular reasoning or fitted constants. Some lemma statements are sloppy (Lemma 9 has a repeated term; Lemma 10's proof ends with a citation to the next lemma), but these are fixable. The lack of a lower bound makes \"near-optimal\" in Remark 4 an overclaim; no lower bound for this problem is known to me, so the authors should soften that.\n\nWho gets value: researchers in bandit pure exploration, principal-agent learning, and scoring rule design will want to know this result. It deserves referee time, but the authors must be held to the advertised-bound mismatch. I would send it out, with a clear request to either prove the stronger bound or restate the claim, and to correct the OIAFB pseudocode. I would not cite the current version's headline claim in my own work.","headline":"Real gap between advertised and proven instance-dependent bounds, and a reversed condition in the fixed-budget pseudocode, but the approach is substantive and merits a major-revision path through peer review.","tokens_in":31546,"tokens_out":5882,"would_cite":false,"duration_ms":44342,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68Q32","68W27"],"pacs":[],"model":"deepseek-v4-flash","headline":"OIAFC identifies an $(\\epsilon,\\delta)$-optimal scoring rule with instance-dependent sample complexity $\\tilde{O}(\\varepsilon^{-2}B_S^2 M H_\\Delta)$, and OIAFB matches the instance-independent rate under a fixed budget.","keywords":["best scoring rule identification","principal-agent information acquisition","online learning","fixed confidence","fixed budget","sample complexity","proper scoring rules","UCB-LP"],"falsifier":"Simulate OIAFC on a synthetic instance with known belief distributions $q_k$, costs $c_k$, and oracle rules $\\tilde{S}_k$; vary the oracle margin $\\varepsilon$ and the suboptimality gaps $\\Delta_k$, and count rounds $\\tau$ until the stopping rule fires. The theorem predicts $\\tau \\approx \\varepsilon^{-2}B_S^2 M H_\\Delta$ up to logarithmic factors with probability at least $1-\\delta$; a materially different scaling, or a successful identification when $\\varepsilon=0$ and no oracle is supplied, would put the central claim in doubt.","tokens_in":30351,"feed_emoji":"🎯","tokens_out":15705,"duration_ms":106460,"temperature":0.7,"pith_summary":"The paper addresses best scoring rule identification (BSRI): a principal interacts repeatedly with an agent who gathers information, and must output a scoring rule that is within $\\epsilon$ of optimal in the principal's profit with confidence at least $1-\\delta$. It proposes OIAFC (fixed confidence) and OIAFB (fixed budget) and proves that both identify an $(\\epsilon,\\delta)$-optimal scoring rule with sample complexity $\\tilde{O}(\\varepsilon^{-2}B_S^2 M H)$, where $H$ is the instance-dependent problem complexity $H_\\Delta = 4(B_S+B_u)^2(\\epsilon^{-2}+\\sum_{k\\neq k^*}\\Delta_k^{-2})$ or the instance-independent $H_\\epsilon = 4(B_S+B_u)^2K/\\epsilon^2$, and $M$ is the size of the belief-report support, at most $K \\times C_{\\mathcal{O}}$. These are, to the authors' knowledge, the first instance-dependent sample-complexity upper bounds for BSRI in this online principal-agent model, and they bring the cost of strategic information acquisition down to the familiar $\\tilde{O}(\\epsilon^{-2})$ form of best-arm identification in multi-armed bandits, up to problem-specific constants. A reader would care because the previous online bound of Chen et al. (2023) was instance-independent and substantially larger, so the extra strategic layer need not multiply the sample cost.","feed_headline":"Algorithms match best-arm rates to find optimal scoring rules","feed_subtitle":"Two algorithms match standard best-arm identification rates in both fixed-confidence and fixed-budget settings.","key_machinery":"The load-bearing objects are the action-informed oracle of Assumption 1, which supplies $K$ scoring rules $\\tilde{S}_k$ such that announcing $\\tilde{S}_k$ makes arm $k$ the agent's best response with a profit margin at least $\\varepsilon$; the optimistic linear program UCB-LP$_{k,t}$, built from estimated belief distributions, estimated pairwise cost differences, and confidence radii, whose optimum is a high-probability upper bound on $h(S^*_k)$; the conservative sampling rule $S_t = \\alpha_t \\tilde{S}_{k^*} + (1-\\alpha_t)\\hat{S}_{k^*,t}$, which biases the agent toward the estimated best arm; and the binary search on the segment between $\\hat{S}_{k^*,t}$ and $\\tilde{S}_{k^*}$ that locates the switching boundary of the response region. The trade-off parameters $\\alpha_t^k$ and the breaking threshold $\\beta_t$ balance normal exploration rounds against forced-exploration binary searches, and the profit gaps $\\Delta_k = h(S^*)-h(S^*_k)$ determine the instance-dependent complexity $H_\\Delta$.","core_discovery":"At the center is a reduction of the principal-agent information acquisition problem to a bandit-like problem in which each arm $k$ has a value $h(S^*_k)$, the principal's maximum profit when the agent's best response is $k$. The principal learns the belief distribution $q_k$ and pairwise cost differences $C(k,k')$ from interactions, builds a linear program UCB-LP$_{k,t}$ whose optimum $\\hat{h}^k_t$ upper-bounds $h(S^*_k)$ with high probability, and each round announces a conservative mixture $S_t = \\alpha_t \\tilde{S}_{k^*} + (1-\\alpha_t)\\hat{S}_{k^*,t}$ of the action-informed oracle rule and the current LP solution. If the agent deviates from the intended arm, a binary search on the line segment between the two rules refines the boundary of the response region $V_k$. With $\\alpha_t^k = \\min(\\sqrt{M/L_t^k},1)$ and a stopping threshold $\\beta_t$, Theorem 1 bounds total rounds by $\\tilde{O}(\\varepsilon^{-2}B_S^2 M H_\\Delta)$ with probability at least $1-\\delta$; Corollary 1 gives $\\tilde{O}(\\varepsilon^{-2}B_S^2 M H_\\epsilon)$ when $\\alpha$ is constant; Theorem 2 and Corollary 2 show OIAFB achieves the same instance-independent rate under a fixed budget.","pith_inferences":["The paper treats the oracle margin $\\varepsilon$ as a fixed constant separate from the accuracy $\\epsilon$; an implicit consequence is that if the oracle is only guaranteed to work with a much smaller margin, the forced-exploration term $\\varepsilon^{-2}$ in Theorem 1 would dominate, so the algorithm's practical efficiency depends on the oracle's quality, not only on the reward gaps.","Because the entire method is built from confidence radii for belief distributions and cost differences, a natural testable extension is to learn the action-informed rules themselves from scratch and use the LP solutions as surrogates; the paper's cited hard instance suggests this can only work under additional structure, so measuring the degradation would clarify how essential the oracle is.","The same UCB-LP machinery could be transferred to multi-agent versions of the problem, since the two incentive constraints (choose the intended arm and report truthfully) are already handled by separate constraints in the linear program; the paper names this direction as future work."],"forward_implications":["If Theorem 1 is correct, instances with well-separated suboptimal arms are solved faster than the worst case, because the sample count depends on $\\sum_{k\\neq k^*}\\Delta_k^{-2}$ rather than only on $K$.","If Corollary 1 is correct, the instance-independent sample complexity improves the previous online bound by removing a large polynomial gap and lands at the same form as classic fixed-confidence best-arm identification, up to the factor $M$ and constants.","If Theorem 2 and Corollary 2 are correct, a principal can commit in advance to a fixed budget $T=\\tilde{O}(\\varepsilon^{-2}B_S^2 M H_\\epsilon)$ and still obtain the same $(\\epsilon,\\delta)$ identification guarantee.","The paper's analysis treats fixed confidence and fixed budget with the same complexity notion, suggesting that the choice between the two settings does not change the fundamental sample cost of the problem."],"supporting_citations":[{"why":"Supplies the online principal-agent information acquisition model, the action-informed oracle assumption, the prior instance-independent BSRI bound that OIAFC improves, and the hard instance showing the oracle is needed.","marker":"Chen et al. (2023)"},{"why":"Provides the $\\ell^1$ concentration inequality for empirical distributions used to construct the confidence radius $I_q^t(k)$ for belief estimators.","marker":"Mardia et al. (2018)"},{"why":"Gives the PAC best-arm identification baseline $\\tilde{O}(K\\epsilon^{-2})$ that OIAFC's instance-independent bound is designed to align with.","marker":"Even-Dar et al. (2002)"},{"why":"Provides a fixed-confidence best-arm identification algorithm whose sample-complexity form is the reference point for the paper's instance-dependent and instance-independent claims.","marker":"Kalyanakrishnan et al. (2012)"},{"why":"Prior online information acquisition work focused on regret and explore-then-commit; the paper contrasts its own fixed-budget analysis and names multi-agent hiring as a future direction.","marker":"Cacciamani et al. (2023)"},{"why":"Source of the termination rule used in Chen et al. (2023), which OIAFC replaces with its own breaking and decision rules to obtain the improved sample complexity.","marker":"Jin et al. (2018)"},{"why":"Defines proper scoring rules, which the paper uses to justify that the agent reports its belief truthfully without loss of generality.","marker":"Savage (1971)"},{"why":"The revelation principle is used to restrict the principal's search to proper scoring rules, a step that underpins the linear program formulation.","marker":"Myerson (1979)"}],"fun_headline_variants":["Scoring rule search matches best-arm identification rates","Best-arm speed for scoring rule learning","Matching best-arm bounds for scoring rule selection","Provably efficient scoring rule via bandit reduction"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire sample-complexity argument assumes a fixed action-informed oracle that provides, for each of the agent's actions, a scoring rule that makes that action strictly best with a profit margin of at least $\\varepsilon$; if such an oracle does not exist or that margin is tiny, the forced-exploration analysis and the $\\varepsilon^{-2}$ factors in the bounds no longer hold.","fun_headline_variants_meta":{"raw":{"variants":["Scoring rule search matches best-arm identification rates","Best-arm speed for scoring rule learning","Matching best-arm bounds for scoring rule selection","Provably efficient scoring rule via bandit reduction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000681,"raw_usage":{"total_tokens":3096,"prompt_tokens":951,"completion_tokens":2145,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":567,"completion_tokens_details":{"reasoning_tokens":2088}},"tokens_in":567,"tokens_out":2145,"duration_ms":13973,"temperature":1.0,"reasoning_tokens":2088,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:48:27.843638+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate OIAFC on a synthetic instance with known belief distributions $q_k$, costs $c_k$, and oracle rules $\\tilde{S}_k$; vary the oracle margin $\\varepsilon$ and the suboptimality gaps $\\Delta_k$, and count rounds $\\tau$ until the stopping rule fires. The theorem predicts $\\tau \\approx \\varepsilon^{-2}B_S^2 M H_\\Delta$ up to logarithmic factors with probability at least $1-\\delta$; a materially different scaling, or a successful identification when $\\varepsilon=0$ and no oracle is supplied, would put the central claim in doubt.","supporting_citations":[{"cited_title":"Learning to incentivize information acquisition: Proper scoring rules meet principal-agent model","cited_arxiv_id":null,"evidence_quote":"Supplies the online principal-agent information acquisition model, the action-informed oracle assumption, the prior instance-independent BSRI bound that OIAFC improves, and the hard instance showing the oracle is needed."},{"cited_title":"Pac bounds for multi-armed bandit and markov decision processes","cited_arxiv_id":null,"evidence_quote":"Gives the PAC best-arm identification baseline $\\tilde{O}(K\\epsilon^{-2})$ that OIAFC's instance-independent bound is designed to align with."},{"cited_title":"Pac subset selection in stochastic multi-armed bandits","cited_arxiv_id":null,"evidence_quote":"Provides a fixed-confidence best-arm identification algorithm whose sample-complexity form is the reference point for the paper's instance-dependent and instance-independent claims."},{"cited_title":"Online Information Acquisition: Hiring Multiple Agents","cited_arxiv_id":"2307.06210","evidence_quote":"Prior online information acquisition work focused on regret and explore-then-commit; the paper contrasts its own fixed-budget analysis and names multi-agent hiring as a future direction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the termination rule used in Chen et al. (2023), which OIAFC replaces with its own breaking and decision rules to obtain the improved sample complexity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines proper scoring rules, which the paper uses to justify that the agent reports its belief truthfully without loss of generality."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The revelation principle is used to restrict the principal's search to proper scoring rules, a step that underpins the linear program formulation."}],"review_version":1}