arxiv: 2604.14465 · v1 · submitted 2026-04-15 · 💻 cs.AI

Recognition: unknown

Improving Human Performance with Value-Aware Interventions: A Case Study in Chess

Saumik Narayanan , Raja Panjwani , Siddhartha Sen , Chien-Ju Ho

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Pith reviewed 2026-05-10 12:40 UTC · model grok-4.3

classification 💻 cs.AI

keywords chessvalue-aware interventionshuman-AI collaborationreinforcement learningpolicy-value discrepancyMarkov decision processhuman performancesequential decision making

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The pith

AI can improve human chess play by intervening on actions that maximize the human value function instead of the engine-optimal move.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that AI assistants should not always recommend the globally optimal action when helping humans in sequential tasks like chess. Instead, they should target interventions where the human's chosen action deviates from the one that maximizes immediate reward plus the value of the resulting state under a model of human behavior. This policy-value discrepancy arises because humans follow suboptimal policies and cannot assume optimal follow-up play, so pure engine-optimal suggestions can reduce overall performance. The approach is formalized in an MDP with a limited intervention budget, with an exact solution for single interventions and a tractable prioritization for multiple ones. Simulations and a 600-game human study confirm that these value-aware interventions raise win rates for low- and mid-skill players while matching expert-engine interventions for high-skill players.

Core claim

We propose value-aware interventions motivated by the Bellman equation: when a human follows a suboptimal policy, discrepancies between the policy-chosen action and the action maximizing immediate reward plus next-state value identify beneficial intervention points. In an MDP where the AI may override under a budget, the single-intervention optimum is to recommend the action maximizing the human value function; for multiple interventions a tractable approximation prioritizes largest discrepancies. Learned from large-scale chess data, this method outperforms Stockfish-based interventions in simulation and, in a within-subject study with 20 players and 600 games, significantly improves low- to

What carries the argument

Policy-value discrepancy: the gap between the action selected by the learned human policy and the action that maximizes immediate reward plus the value of the next state under the learned human value function; this gap flags high-value intervention opportunities.

Load-bearing premise

Models of human policy and value function learned from large-scale gameplay data accurately capture the decision-making and future performance of the specific players in the human study, and policy-value discrepancies reliably identify beneficial intervention opportunities under the budget.

What would settle it

In a replication of the within-subject 600-game human study, value-aware interventions produce no statistically significant win-rate improvement over Stockfish interventions for low- and mid-skill players.

Figures

Figures reproduced from arXiv: 2604.14465 by Chien-Ju Ho, Raja Panjwani, Saumik Narayanan, Siddhartha Sen.

**Figure 1.** Figure 1: Win rate and standard error of each single-intervention strategy across ratings. We evaluate each of these strategies at 100k random positions from sampled from games played by players at 800, 1200, 1600, 2000, and 2400 ratings (500k positions in total), and report the resulting win rate and standard error of each intervention strategy in [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 2.** Figure 2: Win rate of each multipleintervention strategy across player ratings and intervention frequency budgets. Overall, our results align with our expectations on the relationship between intervention frequency and performance for both strategies. At each player rating, Valuemax outperforms Stockfish at small intervention budgets. For instance, for 800-rated players, Valuemax outperforms Stockfish with budget… view at source ↗

**Figure 3.** Figure 3: Human performance of each intervention strategy across ratings. In this work, we study how AI systems should intervene when assisting humans in sequential decision-making tasks. While a natural baseline is to recommend the action from a strong expert model, such recommendations implicitly assume optimal continuation. When human decision makers deviate from optimal play, these recommendations may lead … view at source ↗

read the original abstract

AI systems are increasingly used to assist humans in sequential decision-making tasks, yet determining when and how an AI assistant should intervene remains a fundamental challenge. A potential baseline is to recommend the optimal action according to a strong model. However, such actions assume optimal follow-up actions, which human decision makers may fail to execute, potentially reducing overall performance. In this work, we propose and study value-aware interventions, motivated by a basic principle in reinforcement learning: under the Bellman equation, the optimal policy selects actions that maximize the immediate reward plus the value function. When a decision maker follows a suboptimal policy, this policy-value consistency no longer holds, creating discrepancies between the actions taken by the policy and those that maximize the immediate reward plus the value of the next state. We show that these policy-value inconsistencies naturally identify opportunities for intervention. We formalize this problem in a Markov decision process where an AI assistant may override human actions under an intervention budget. In the single-intervention regime, we show that the optimal strategy is to recommend the action that maximizes the human value function. For settings with multiple interventions, we propose a tractable approximation that prioritizes interventions based on the magnitude of the policy-value discrepancy. We evaluate these ideas in the domain of chess by learning models of humans from large-scale gameplay data. In simulation, our approach consistently outperforms interventions based on the strongest chess engine (Stockfish) in a wide range of settings. A within-subject human study with 20 players and 600 games further shows that our interventions significantly improve performance for low- and mid-skill players while matching expert-engine interventions for high-skill players.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes value-aware interventions for AI-assisted sequential decision-making, motivated by the Bellman equation: when a human follows a suboptimal policy, discrepancies arise between actions taken and those maximizing immediate reward plus next-state value. These discrepancies identify intervention opportunities under a budget. In chess, human policy and value models are learned from large-scale data. Simulations show the method outperforming Stockfish-based interventions across settings. A within-subject human study (20 players, 600 games) reports significant performance gains for low- and mid-skill players while matching expert-engine interventions for high-skill players.

Significance. If the results hold, the work supplies a principled RL-derived framework for AI assistance that accounts for human suboptimality rather than assuming optimal follow-through, with clear implications for domains beyond chess. The direct derivation from the Bellman equation and dual validation via simulation plus human data are strengths that enhance the contribution.

major comments (2)

[Human study section] Human study section: The central claim of performance improvement for low- and mid-skill players rests on population-level models of human policy π_h and value V_h (trained on aggregate data) correctly identifying discrepancies that produce actual gains for the specific 20 study participants. No per-participant calibration, hold-out validation on their non-intervention games, or comparison of predicted vs. observed value is reported. This assumption is load-bearing for linking the intervention rule to the observed Elo/win-rate gains.
[Section 3] Multiple-intervention approximation (Section 3): The tractable prioritization by discrepancy magnitude is used for the simulation results claiming consistent outperformance over Stockfish interventions. However, no error analysis, bounds, or empirical comparison to exact multi-step optimization is provided, which is necessary to substantiate robustness across the reported range of intervention budgets and settings.

minor comments (2)

[Abstract] Abstract and methods: Training details for the human policy and value models (dataset size, architecture, validation procedure) are not summarized, which would aid reproducibility.
[Results] Results presentation: The human-study outcomes are summarized at a high level; adding error bars, exact p-values, and per-skill-level breakdowns by intervention count would improve clarity without altering the claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive review. The comments highlight important aspects of our methodology and evaluation. We address each major comment below and outline the revisions we will make to the manuscript.

read point-by-point responses

Referee: [Human study section] Human study section: The central claim of performance improvement for low- and mid-skill players rests on population-level models of human policy π_h and value V_h (trained on aggregate data) correctly identifying discrepancies that produce actual gains for the specific 20 study participants. No per-participant calibration, hold-out validation on their non-intervention games, or comparison of predicted vs. observed value is reported. This assumption is load-bearing for linking the intervention rule to the observed Elo/win-rate gains.

Authors: We acknowledge that our human policy and value models are trained on large-scale aggregate data rather than being calibrated per participant. This approach allows us to leverage extensive gameplay data for more reliable estimates of human behavior, which would be challenging with the limited games per player in the study. The within-subject human study with 600 games across 20 players provides empirical evidence that these models lead to performance improvements. To strengthen the manuscript, we will add a discussion in the human study section addressing the use of population-level models, including any available validation from the training data splits, and note this as a direction for future personalized interventions. revision: partial
Referee: [Section 3] Multiple-intervention approximation (Section 3): The tractable prioritization by discrepancy magnitude is used for the simulation results claiming consistent outperformance over Stockfish interventions. However, no error analysis, bounds, or empirical comparison to exact multi-step optimization is provided, which is necessary to substantiate robustness across the reported range of intervention budgets and settings.

Authors: We agree that providing additional analysis for the multiple-intervention approximation would enhance the robustness claims. The prioritization heuristic is motivated by the optimality in the single-intervention case and the Bellman discrepancy principle. In the revised manuscript, we will include an empirical comparison of the approximation against exact multi-step optimization (via dynamic programming) for a subset of settings with smaller budgets where exact computation is tractable. We will also add a brief discussion on the approximation's rationale and potential error sources. revision: yes

Circularity Check

0 steps flagged

Derivation from Bellman equation is independent of fitted human models

full rationale

The paper's core derivation begins from the Bellman equation to identify policy-value discrepancies as intervention opportunities in an MDP with intervention budget, then proves that the optimal single-intervention strategy is to select the action maximizing the human value function. This step is a direct mathematical consequence of the optimality principle and does not reduce to or depend on any fitted parameters, data, or self-citations. Human policy and value models are subsequently learned from large-scale chess data solely to instantiate the rule in the domain; simulation and human-study evaluations apply the rule against external baselines (Stockfish) and real participants rather than re-deriving or tautologically confirming the rule from the same fits. No self-citation chains, uniqueness theorems, or ansatzes are used to justify the central claims, and the empirical results remain falsifiable outside the fitted values.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, limiting visibility into exact parameters; the approach rests on the standard Bellman optimality equation and data-driven human models whose fitting details are unspecified.

axioms (1)

standard math Bellman equation holds for the optimal policy in the MDP
Invoked to define policy-value consistency and identify intervention opportunities.

pith-pipeline@v0.9.0 · 5605 in / 1170 out tokens · 40346 ms · 2026-05-10T12:40:35.669341+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

6 extracted references · 3 canonical work pages

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Learning to make adherence- aware advice.arXiv preprint arXiv:2310.00817,

Guanting Chen, Xiaocheng Li, Chunlin Sun, and Hanzhao Wang. Learning to make adherence- aware advice.arXiv preprint arXiv:2310.00817,

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Reinforce- ment learning interventions on boundedly rational human agents in frictionful tasks

Eura Nofshin, Siddharth Swaroop, Weiwei Pan, Susan Murphy, and Finale Doshi-Velez. Reinforce- ment learning interventions on boundedly rational human agents in frictionful tasks. InPro- ceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems: AAMAS. International Joint Conference on Autonomous Agents and Multiagent Syste...

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Narrowing action choices with ai improves human sequential decisions.arXiv preprint arXiv:2510.16097,

Eleni Straitouri, Stratis Tsirtsis, Ander Artola Velasco, and Manuel Gomez-Rodriguez. Narrowing action choices with ai improves human sequential decisions.arXiv preprint arXiv:2510.16097,

work page arXiv
[4]

Human-aligned chess with a bit of search.arXiv preprint arXiv:2410.03893,

Yiming Zhang, Athul Paul Jacob, Vivian Lai, Daniel Fried, and Daphne Ippolito. Human-aligned chess with a bit of search.arXiv preprint arXiv:2410.03893,

work page arXiv
[5]

All code is available at https://anonymous.4open.science/r/value-aware-interventions-0C08/

A Model Training Details In this section, we provide more details on the BC model used for all simulated analysis in the paper. All code is available at https://anonymous.4open.science/r/value-aware-interventions-0C08/. A.1 Dataset Construction All data is taken from the Lichess online database, which contains over 7.5 billion chess games played by humans...

2024
[6]

B Exploring Human-Understandable Concepts in Our Interventions One advantage of studying interventions in the domain of chess is that positions can be evaluated using a large number of structured, human-understandable concepts derived from classical chess evaluation functions. Modern engines such as Stockfish compute hundreds of intermediate features that...

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