Title: Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty
Venue: NeurIPS 2025
Accepted: yes
Keywords: strategic classification

causality

uncertainty

desirable effort

classifier design
Abstract: We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in one feature may affect other features. The main goal of our work is to understand when and how much agent effort is invested towards desirable features, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them,  and the information available to the agent about the classifier and the feature causal graph. We characterize conditions under which agents with full information about the causal structure and the principal's classifier align with the principal's goals of incentivizing effort mostly in ``desirable'' features, and identify cases where designing such classifiers (from the principal's side) is still tractable despite general non-convexity. Under incomplete information, we show that uncertainty leads agents to prioritize features with high expected impact and low variance, which may often be misaligned with the principal's goals. Finally, using numerical experiments based on a cardiovascular disease risk study, we illustrate how to incentivize desirable modifications even under uncertainty.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new formulation of SC based on a causal perspective. Specifically, the causal effects of investing efforts are captured by a contribution matrix $C$ and the decision maker publishes a linear classifier $h$. The cost is formulated as the weighted $L_p$ norm of the effort. The paper first characterized the optimal effort profiles when agents best respond under a complete information setting, and pointed out that space of desired classifiers is non-convex/convex when the set of desirable features has cardinality $>1$/$1$. Finally, the paper discussed two settings of incomplete information and gave explicit expressions of the optimal effort profile under when the cost is $l_2$.\n\nSTRENGTHS AND WEAKNESSES:\n> Strengths\n- The problem formulation is reasonable and the theoretical results seem to be solid.\n- The consideration of incomplete information is interesting.\n- The writing is clear.\n\n> Weaknesses\n- The formulation of the causal structure is still similar to [23] although [23] did not mention \"causal\". The causal effects are still characterized by the multiplication of $C$ and $e$. But the causal effects in reality can be more complex (e.g., non-linear)\n- Getting the contribution matrix $C$ may be difficult in practice, so it may be worthwhile adding such a discussion on the practical usage.\n- Some highly related works are not mentioned. For example, [1] discussed long-term genuine improvement in SC settings, while [2] discussed the externalities of SC.\n\n[1] Xie, T., Tan, X., & Zhang, X. (2024, October). Algorithmic decision-making under agents with persistent improvement. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society (Vol. 7, pp. 1672-1683).\n\n[2] Hossain S, Micha E, Chen Y, et al. Strategic classification with externalities[J]. arXiv preprint arXiv:2410.08032, 2024.\n\nQUESTIONS:\n1. Are there efficient algorithms to learn an optimal classifier to incentivize desirable efforts in your problem setting, especially when there is incomplete information?\n2. Can you discuss with learning the contribution matrix $C$ in practice?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a causal framework for strategic classification in which agents invest effort to modify features that influence others, and a principal wants to steer that effort toward desirable attributes. It introduces $\\beta$-desirability to quantify the share of effort on preferred features, characterizes agents’ optimal effort under $\\ell_p$ costs, and derives sufficient conditions on linear classifiers that guarantee desirable behavior under full information. The authors show finding such classifiers is generally non-convex but becomes convex when one feature is targeted, and they analyze partial-information settings, providing closed-form responses and numerical experiments on cardiovascular-risk data to validate their theory.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n* Well-structured paper.  Clear separation of complete vs. incomplete information.\n  \n* Combines causal modelling with strategic classification under uncertainty—areas that had largely been studied separately.\n  \n* Good intuitive explanations. After each theorem the authors add discussion.\n  \n* All main results are formally stated with complete assumptions and full proofs in the appendix.\n  \n\n## Weaknesses\n\n* **Causal Structure**:  The entire DAG topology is assumed common knowledge; in practice, agents seldom know the full graph structure.\n  \n* **Feature Dynamics**: The framework relies on linear causal relations encoded in a contribution matrix $C$, whereas real-world effects are often non-linear or state-dependent.\n  \n* **Finite Sample**: The paper does not address how estimation error in the DAG would affect the results.\n  \n* **$\\beta$-Desirable**: just only large amount of $\\beta$-desirable provied gurantee to use desirable faetures instead of undesireable feature\n  \n* **Classifier Family**: Analysis is limited to linear classifiers with a fixed threshold, while non-linear models (trees, neural nets) dominate many real applications.\n  \n* **Agent information**: Agents’ beliefs over $h$ and edge weights are assumed Gaussian, yet empirical priors are often multi-modal or heavy-tailed.\n  \n* **Non-convex design problem.** The desirable-classifier search is non-convex except when $|D| = 1$ and $p \\le 3$; the paper provides only a heuristic with no guarantees in the general case.\n  \n* **Agent optimisation hardness.** Under full uncertainty the best-response program is non-convex (they show even the simple 2-feature toy becomes non-concave) , but no algorithmic remedy is proposed.\n  \n* **Algorithmic Recourse**: Despite close ties, the paper does not reference the algorithmic recourse literature.\n  \n* **Simulation**: The only experiment uses one expert-elicited CVD DAG with eight features; no cross-domain validation, no real behavioural data, and no statistical uncertainty.\n\nQUESTIONS:\n- Your model presumes agents know the entire causal-graph topology. How would the guarantees change if this topology were uncertain or misspecified?\n\n- How does the proposed method scale as the number of features $d$ grows large?\n\n- The empirical study uses only one eight-feature CVD graph. Can you provide additional experiments on public strategic-behaviour datasets (e.g., credit scoring, résumé screening) to demonstrate external validity?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses strategic classification under causal interdependencies and incomplete information. It introduces the concept of β-desirable effort profiles and analyzes how rational agents respond to deployed classifiers under different information assumptions. The authors consider both complete and incomplete knowledge settings and provide a combination of theoretical results and simulations based on cardiovascular disease prediction. The model incorporates causal graphs, agent cost functions, and effort optimization, providing insight into classifier design that incentivizes desirable (rather than merely effective) changes.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n- The problem is important and well-motivated: incentivizing desirable feature change under strategic manipulation is a key issue in responsible ML.\n- Strong theoretical depth with clean characterizations (e.g., β-desirability conditions).\n- Good mix of theory and simulation; the cardiovascular disease application is relevant and realistic.\n- Reasonable modeling assumptions around cost functions, agent behavior, and effort optimization.\n- Good literature coverage (in Appendix) but also in main body when contrasting against most similar work.\n\n### Weaknesses\n- At times, the paper is dense and difficult to read — many sections could benefit from simplification or intuitive summarization of key ideas. E.g., several concepts (e.g., β-desirability, agent best response, contribution matrix) take effort to parse and might deter less technical readers.\n- While the related work is thorough, it lacks direct contrast with causal algorithmic recourse literature — a striking omission given the similarity in goals. Esp. since those works operate on models beyond the linear variants studied here\n- The empirical section is clean, but could benefit from a broader discussion of fairness and real-world risks.\n\nQUESTIONS:\n1. Could the authors contrast this work more clearly with the literature on causal algorithmic recourse (e.g., [Mothilal et al., 2020], [Karimi et al., 2021])? The lack of mention is surprising given the shared setting.\n2. Are there cases where the incentive structure leads to undesirable gaming behavior under partial information? A small example would be helpful.\n3. The β-desirability conditions are mathematically clean — could the authors comment on the extent to which principals can reasonably verify them in practice?\n4. Line 90: is it that the features are desirable/undesirable, or changes to/interventions upon those features?\n5. How would the framework handle heterogeneous populations (e.g., different groups with different priors or cost sensitivities)?\n\nLIMITATIONS:\nNo — while section 6 does speak to the methodology's limitations, more explicit discussing regarding the practicality of assuming full causal graph knowledge and cost function specifications, as well as risks tied to fairness, misspecification, and strategic disparity would be welcome.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors consider a binary classification with strategic agents. The agents can exert effort to get desired decision. The author also consider a scenario where there are desirable and undesirable features and investigate how the classifier can lead to improving desirable features. \n\nThe authors considers both complete and incomplete information and provide insight on the best response function of the agents.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: The paper is well written. It is easy to follow and can provide some insight on how strategic classification works.\n\nWeaknesses: \n\n1. The scenario that they consider is very simple. While it is in the context of  machine learning, basically the authors consider a very simple two stage game between decision maker and an agent. The first order condition is used to find the best response. \n\n2. The scenario looks very superficial. A scenario with liner classifier and know causal graph. It is not clear in what real world problem, we can apply this study. \n\n3. In the incomplete information case, still the authors assume the agent knows the distribution over hypothesis space. This still gives a lot of information to agent leading to optimization problem 4.\n\n4. No discussion on how the design maker should find the optimal classifier. The authors discuss that the problem is non-convex for the design maker. But no further insight or algorithm provided for solving that problem. \n\n5. No discussion on how the results can be extended to non-linear case or a scenario where the agents are interdependent.\n\nQUESTIONS:\n1. In what real world problems, the proposed model can be used?\n\n2. How the design maker should find the optimal classifier? How should we define the optimal classifier? Because we want to have \\beta-desirable outcome, we need to clearly define optimal classifier? \n\n3. In the game theory and economics, there is notion of socially optimality. Why we cannot use this concept instead of Desirable Classfier concept proposed here? \n\n4. How the problem can be extended to non-linear case? \n\n5. What the agents are interdependent (effort of one impact others' utility)\n\nLIMITATIONS:\nThe author have not discussed potential negative societal impact (or I could not find).", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}