Fairness Aware Reinforcement Learning via Proximal Policy Optimization

Elizabeth Black; Gabriele La Malfa; Jie M. Zhang; Michael Luck

REVIEW 4 major objections 5 minor 49 references

Fairness Aware Reinforcement Learning via Proximal Policy Optimization

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A two-part fairness penalty added to PPO's objective produces fairer multi-agent policies without sacrificing competitive performance.

desk verdict The prospective value-based fairness penalty is a real idea, but the retrospective α-term in Eq. (6) is formally inert as written, so the paper's central mechanism needs major clarification before the results can be trusted. read the letter →

arxiv 2502.03953 v2 pith:F56LKI27 submitted 2025-02-06 cs.MA cs.LG

Gabriele La Malfa , Jie M. Zhang , Michael Luck , Elizabeth Black This is my paper · ORCID

classification cs.MAcs.LG

keywords fairreinforcementlearningmulti-agentsystemsProximalPolicyOptimizationdemographicparitycounterfactualfairnessconditionalstatisticalAllelopathicHarvestHospitalSim

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that fairness in multi-agent reinforcement learning can be achieved by adding a penalty to the standard PPO objective rather than by designing a new fair algorithm. Fair-PPO penalises the gap between sensitive and non-sensitive groups in two places: the total rewards earned in the just-finished episode and the value estimates the critic assigns to the current state. In the Allelopathic Harvest and HospitalSim environments, the paper reports that Fair-PPO lowers demographic, conditional statistical, and counterfactual disparity relative to PPO, and that its efficiency matches the FEN and SOTO baselines. If correct, the method gives practitioners a two-knob way to move any PPO deployment along a fairness-efficiency frontier.

What carries the argument

The load-bearing object is the modified objective $$$L^{{\mathrm{Fair-PPO}}$}_t(\theta_i) = \hat{\mathbb{E}}_t\left[ $L^{{\mathrm{CLIP}}$}_t(\theta_i) - c_1 $L^{{\mathrm{VF}}$}_t(\theta_i) + c_2 H[\pi_{\theta_i}](s_t) - \$\lambda$ $L^{{\mathrm{fair}}$}_t \right],$$ with the demographic-parity penalty $$$L^{{\mathrm{fair-DP}}$}_t = \$\alpha$\left|\bar{G}_{N_1}(\tau)-\bar{G}_{N_0}(\tau)\right| + \$\beta$\left|\bar{V}_{N_1}(s_t)-\bar{V}_{N_0}(s_t)\right|.$$ The first term is retrospective, using one finished episode's group-average returns; the second is prospective, using the critic's current value estimates. The paper provides analogous penalties for counterfactual fairness and conditional statistical parity. This two-component decomposition is what makes the fairness pressure tunable: $\alpha$ controls reaction to past disparity and $\beta$ controls anticipation of future disparity.

What would settle it

Train Fair-PPO and PPO in HospitalSim on identical patient streams, then re-run the trained policies after randomly permuting the impairment labels; if the disparity reduction persists when the sensitive attribute carries no causal information, the penalty is reducing variance rather than group bias. A cheaper check is to correlate the one-episode reward gap used in Eq. (6) with the 500-episode test disparity and observe whether it is near zero.

Watch

Extended reading notes

Core claim

On its own terms, the central discovery is that a penalty term composed of a retrospective reward-disparity component and a prospective value-disparity component, inserted into the PPO clipped-surrogate objective, is sufficient to shift policies toward fairer reward distribution across groups defined by a sensitive attribute. The retrospective term compares per-episode average total rewards $\bar{G}_{N_1}(\tau)$ and $\bar{G}_{N_0}(\tau)$; the prospective term compares average critic estimates $\bar{V}_{N_1}(s_t)$ and $\bar{V}_{N_0}(s_t)$. The paper reports lower demographic disparity than PPO in both games; in HospitalSim the fairest tested setting cuts demographic disparity from 6.83 to 5.31 while treating 68.69 patients per day instead of 105.92, and in Allelopathic Harvest Fair-PPO matches SOTO on fairness while FEN reaches lower disparity only with much lower rewards and worse Gini. The authors conclude that fairness is purchasable at the cost of efficiency, but not at the cost of overall population equality.

Load-bearing premise

The load-bearing premise is that one episode's difference in total reward between the sensitive and non-sensitive groups, together with the critic's current value estimates, is a trustworthy signal of lasting policy unfairness rather than a sample of environment noise.

Editorial extensions

If this is right

Setting $\alpha=\beta=0$ recovers standard PPO, so Fair-PPO is a strict generalisation of PPO and requires no change to the policy network.
Sweeping $\alpha$ and $\beta$ across $[0,1]$ produces a family of policies with different fairness-efficiency balances, so a user can select an operating point rather than a single fair policy.
Replacing the demographic-parity penalty with the counterfactual or conditional-statistical-parity penalty swaps the fairness notion without changing the training loop.
In HospitalSim, lower demographic disparity came with fewer daily treated patients, so the fairness gain is real but paid for in throughput.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural, untested extension is to anneal or learn $\alpha$ and $\beta$ during training; the HospitalSim grid suggests only a narrow band of settings improves on PPO, which an adaptive schedule might find more reliably.
Because the prospective term depends on the critic, its meaning changes as the critic improves; an implied prediction is that the optimal $\beta$ should shrink over training as value estimates become reliable.
Nothing in the penalty formula restricts it to binary attributes, so applying the same group-disparity penalty to multi-valued or continuous sensitive attributes is a plausible next step, though the paper does not test it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know the main thing first: the retrospective half of the penalty in Eq. (6) is a constant with respect to the policy parameters. G_N1(τ) and G_N0(τ) are scalars from the last episode; their absolute difference has zero gradient through θ. So as written, the α-term cannot change the policy. The paper still reports α-sweeps, including a β=0 case (α=0.25, β=0) that improves disparity, which means the implementation must be doing something not in the equations — perhaps adding the penalty to rewards before computing advantages, or using the dynamic λ in a way that couples α to the critic. None of that is specified. This is a load-bearing hole, not a stylistic one.

What is genuinely new: the prospective term β|V_N1(s_t) - V_N0(s_t)| — using critic estimates as a fairness signal — is a sensible idea I haven't seen in the cited fair-RL literature. The AH experiments, with boxplots, show a real reduction in demographic disparity (0.182/0.159 vs 0.315/0.313 for PPO). HospitalSim is a substantial new environment, and the paper honestly reports the efficiency cost, the Gini index, and a cautious ethical statement.

The soft spots are real but secondary to the gradient issue. The HS results are mixed: most (α,β) settings don't beat PPO's 6.83 disparity, the headline best (5.31) treats only 68.69 patients daily vs 105.92 for PPO, and there are no error bars or significance tests anywhere in Tables 1 and 13. Table 2 shows CSP disparity worse than PPO for two of three priority groups. Also, because Eq. (6) is called the sample-based equivalent of the evaluation metric ΔDP, the primary fairness improvement is partially built into the objective; the independent content is the prospective term and the strategy spectrum.

Who is this for? Researchers working on fairness in multi-agent RL will want to engage, mainly to replicate and to fix the mechanism. The code is available, which is good. But as it stands, the formal description doesn't match the reported results. My recommendation: send to peer review, but flag the Eq. (6) gradient issue explicitly. The authors need to specify how the retrospective term enters the optimization, or remove it and rerun the α-sweep. If they can't, the paper reduces to a single-knob prospective penalty with mixed evidence.

Referee Report

4 major / 5 minor

Summary. The paper proposes Fair-PPO, a modification of PPO that adds a fairness penalty, composed of a retrospective term (comparing last-episode total rewards between sensitive and non-sensitive groups) and a prospective term (comparing value-function estimates), to the PPO loss. The penalty is derived from demographic parity, with analogous penalties for counterfactual fairness and conditional statistical parity in the supplement. The method is evaluated in the Allelopathic Harvest (AH) multi-agent game and in a newly introduced HospitalSim (HS) simulation, and is compared against PPO, FEN, and SOTO. The authors report that Fair-PPO produces fairer policies than PPO, spans a spectrum of fairness-efficiency trade-offs, and that fairness comes at an efficiency cost without worsening the Gini index.

Significance. If the proposed mechanism is correct, Fair-PPO would be a practical, penalty-based approach for injecting group-fairness constraints into PPO for multi-agent systems, and the introduction of HospitalSim could be a useful testbed for fair multi-agent coordination. The paper is also commendable for releasing code and for reporting a wide sweep of the two penalty weights, plus comparisons with two existing fairness-aware MARL methods. However, the central gradient question about Eq. (6) is not a presentation issue: as written, the retrospective term is constant with respect to the policy parameters, so the paper's explanation of how the method works is not supported by the equations. This must be resolved before the empirical claims can be accepted.

major comments (4)

[Section 4, Eq. (6)] The retrospective term α·|Ḡ_N1(τ) − Ḡ_N0(τ)| is computed from the total rewards collected in the last episode, and is therefore a constant with respect to the policy parameters θ_i. In any standard autodiff implementation of the PPO objective, its gradient with respect to θ_i is identically zero, so this term cannot by itself change the policy. This is contradicted by Table 13, where β=0 configurations such as α=0.25, β=0 (disparity 6.52 vs. PPO 6.83) are reported, and by the paper's claim that the retrospective component participates in the fairness mechanism. The supplementary mention of a 'dynamic λ' is not sufficient because λ is never defined. The authors must specify the actual objective used in code (for example, whether the penalty is folded into rewards or advantages before computing returns) and, if the α-term is genuinely used, derive its gradient or show the code path that makes it effective.
[Section 5 (Train) and Eq. (5)] In HospitalSim the fairness penalty is computed from the rewards of patients, who are not learning agents, yet Eq. (5) defines V̄_G(s_t) as the average of value estimates V_θ_i(s_t) over agents i in G. Patients have no policy parameters in the described framework, so it is undefined what V̄_N1(s_t) − V̄_N0(s_t) means for the patient groups and whether it is differentiable with respect to the three learning agents' parameters. The prospective component of the HS results therefore needs a concrete definition, such as a separate patient-value critic, before the reported trade-offs can be attributed to the stated mechanism.
[Table 13 and Section 6] Of the 25 (α, β) configurations in Table 13, only a minority produce demographic disparity below PPO's value of 6.83 (e.g., α=0.25, β=0; α=0.25, β=0.5; α=0.5, β=0.25; α=0.75, β=0.75; α=1.0, β=1.0). Moreover, the best such setting (α=0.5, β=0.25) reduces daily treated patients from 105.92 to 68.69. The abstract's statement that Fair-PPO 'achieves fairer policies than PPO' across the fairness metrics is therefore an overstatement unless it is restricted to selected configurations or accompanied by a demonstration of a systematic trend. Please report the distribution across seeds for all configurations and explicitly quantify the efficiency cost in the headline comparison.
[Section 5 (Train)] The retrospective penalty is computed from a single episode's total returns: a 3000-step AH game or a 12-hour, 300-patient HS day. Given the stochasticity of bush growth in AH and patient arrivals in HS, a one-episode estimate of ΔDP has high variance. If the penalty chases episodic noise rather than a stable policy-level disparity, this would explain why most HS settings do not beat PPO and why the fairest settings collapse efficiency. The paper should validate that the episodic penalty correlates with the long-run evaluation disparity, for example by showing smoothed training curves of the penalty against the evaluation-time ΔDP, or by reporting multiple training seeds.

minor comments (5)

[Abstract and Section 6] The paper claims counterfactual fairness as one of the evaluated fairness notions, but no counterfactual fairness results are reported; only demographic parity and conditional statistical parity tables appear. Please either add the counterfactual fairness experiments or remove the claim from the abstract.
[Section 4, Definition 4.2] The counterfactual system M′ is defined conceptually, but the training procedure for constructing π′ and the meaning of the counterfactual value estimates in Eq. (7) are not described. No experimental implementation of counterfactual fairness is provided.
[Section 5 (Train/Test)] The HS description states that the simulation is event-driven and has no time steps, yet Eq. (6) and the PPO objective use per-timestep quantities indexed by t. Please clarify how episode-level penalties are attached to the timestep-level objective in the event-driven setting.
[Supplementary (Additional Results)] The cross-references to 'Table 6 and 7' in the supplementary text appear to be outdated; the actual supplementary tables are numbered 11–14. Please correct these references.
[Tables 1, 2, and 13] Several table headers concatenate long labels without separators, e.g., 'Fair-PPOα= 0.25, β= 0.25' and 'PatientWait Escort(Minutes)'. This makes the tables difficult to read and should be reformatted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Fair-PPO's fairness penalty intentionally uses the same disparity notion as the evaluation metric, but the paper's claims are supported by independent benchmarks and auxiliary metrics.

full rationale

The derivation chain is not circular. Eq. (6) is introduced as the 'sample-based equivalent of the ∆DP metric,' so improving the evaluated demographic disparity under Fair-PPO is partly a direct consequence of optimizing a penalty with the same structure; that is a by-design property of a fairness-regularized RL objective rather than a 'prediction' that reduces to its inputs. The load-bearing comparisons are not restricted to that single metric: Fair-PPO is benchmarked against FEN and SOTO, and the results are also assessed on Gini index, JFI, NNSW, and efficiency metrics, which are not components of the training penalty. No load-bearing self-citation or imported uniqueness theorem appears; the citations to PPO and to penalized-PPO prior work are background. The differentiability concern raised about the α-term in Eq. (6) (that the retrospective term is constant w.r.t. the policy parameters) is a correctness/implementation issue, not a circularity: it does not make a conclusion equal to its premise. Overall, the paper is self-contained against external baselines, so the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The method rests on reward-parity as the fairness definition (Definitions 4.1-4.3), on the assumption that critic value estimates are reliable prospective fairness signals (Eq. 6 prospective term), on the stationarity of per-episode disparity signals in two non-stationary simulations, and on the unvalidated realism of the new HospitalSim environment. The free parameters are the two penalty weights α and β (swept and selected per metric) and the unspecified dynamic λ.

free parameters (3)

α (retrospective penalty weight) = 0.0 to 1.0 in steps of 0.25; best per metric selected for headline tables
Controls the weight on past-reward disparity in Eq. 6. The reported fairness gains depend on selecting favorable values per metric from the 25-point sweep.
β (prospective penalty weight) = 0.0 to 1.0 in steps of 0.25; best per metric selected for headline tables
Controls the weight on value-estimate disparity in Eq. 6. Same selection-dependence as α.
λ (fairness penalty magnitude) = unspecified (described only as 'dynamic')
Balances the fairness penalty against the standard PPO loss. No formula or schedule is given in the paper or supplementary material.

assumptions (5)

domain assumption Group fairness is defined as parity of average expected rewards between agents partitioned by a binary sensitive attribute
Definitions 4.1-4.3 adopt reward parity as the fairness notion; the entire method optimizes and evaluates this parity, so the paper's fairness claims presuppose this definition.
domain assumption The value function estimates provide a valid prospective fairness signal
The prospective penalty term β|V_N1 - V_N0| (Eq. 6) assumes critic estimates are informative early in training; the paper motivates the prospective term by the insufficiency of retrospective rewards but does not validate value-estimate reliability.
standard math PPO clipped surrogate objective and its convergence properties are taken as given
Section 3 adopts Schulman et al. 2017 PPO; the fairness analysis inherits PPO's stability assumptions without modification.
domain assumption Per-episode aggregate reward disparities are stationary and unbiased across episodes
In both environments the penalty is computed per episode (3000 steps in AH, one hospital day in HS) and averaged; non-stationarity from resource dynamics (AH bush growth/death) or stochastic patient mix (HS) could make single-episode disparities noisy proxies for long-run group parity.
domain assumption HospitalSim's synthetic reward structure is a meaningful proxy for real hospital fairness
HS is an original simulator with no calibration to real hospital data; the Ethical Statement acknowledges the sensitive-attribute simplification and that findings are not a direct basis for policy.

invented entities (1)

HospitalSim (HS)
purpose: A new three-agent hospital coordination simulation to evaluate Fair-PPO in a non-competitive MAS; provides patient-level reward disparity metrics
HS is constructed by the authors for this paper; its patient flows, ward mappings, and reward weights (Tables 4-6 of the supplementary) are not validated against real hospital data, and the paper itself cautions against using findings as a policy basis.

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Cite this review

Pith. "Pith review of Fairness Aware Reinforcement Learning via Proximal Policy Optimization." pith.science (2026). https://pith.science/paper/F56LKI27

@misc{pith2026250203953,
  author       = {Pith},
  title        = {Pith review of: Fairness Aware Reinforcement Learning via Proximal Policy Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F56LKI27}},
  note         = {Machine review of arXiv:2502.03953}
}

read the original abstract

Fairness in multi-agent systems (MAS) focuses on equitable reward distribution among agents in scenarios involving sensitive attributes such as race, gender, or socioeconomic status. This paper introduces fairness in Proximal Policy Optimization (PPO) with a penalty term derived from a fairness definition such as demographic parity, counterfactual fairness, or conditional statistical parity. The proposed method, which we call Fair-PPO, balances reward maximisation with fairness by integrating two penalty components: a retrospective component that minimises disparities in past outcomes and a prospective component that ensures fairness in future decision-making. We evaluate our approach in two games: the Allelopathic Harvest, a cooperative and competitive MAS focused on resource collection, where some agents possess a sensitive attribute, and HospitalSim, a hospital simulation, in which agents coordinate the operations of hospital patients with different mobility and priority needs. Experiments show that Fair-PPO achieves fairer policies than PPO across the fairness metrics and, through the retrospective and prospective penalty components, reveals a wide spectrum of strategies to improve fairness; at the same time, its performance pairs with that of state-of-the-art fair reinforcement-learning algorithms. Fairness comes at the cost of reduced efficiency, but does not compromise equality among the overall population (Gini index). These findings underscore the potential of Fair-PPO to address fairness challenges in MAS.

Figures

Figures reproduced from arXiv: 2502.03953 by the authors.

**Figure 2.** Allelopathic Harvest: Fair-PPO (α, β) demographic disparity boxplots clusters (light pink, purple and dark purple) and the Price of Fairness vs. PPO. that heavily prioritises ripening the bush, which is the action most beneficial for other agents collecting rewards. The highest disparity (dark purple) focuses more on berry consumption, the selfish action. SOTO reaches similar fairness results to Fair-PPO with low… view at source ↗

**Figure 3.** Allelopathic Harvest. Fair algorithms’ performance (average demographic disparity and Gini index) for each archi [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Allelopathic Harvest. Action frequencies of Fair [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: HospitalSim. Fairness (demographic disparity) and [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Allelopathic Harvest. Fairness (conditional statistical parity), Gini index and NNSW for Fair-PPO and benchmarks [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: Allelopathic Harvest. Fairness (conditional statistical parity), Gini index and NNSW for Fair-PPO and benchmarks [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

[3] [3]

Amanatidis, G.; Aziz, H.; Birmpas, G.; and et al. 2023. Fair division of indivisible goods: Recent progress and open questions. Artificial Intelligence, 322: 103965

work page 2023

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Baker, R.; and Hawn, A. 2021. Algorithmic Bias in Education. International Journal of Artificial Intelligence in Education, 32

work page 2021

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Barman, S.; Khan, A.; Maiti, A.; and Sawarni, A. 2023. Fairness and welfare quantification for regret in multi-armed bandits. In AAAI'23/IAAI'23/EAAI'23, AAAI'23/IAAI'23/EAAI'23. ISBN 978-1-57735-880-0

work page 2023

[6] [6]

Berk, R. 2019. Accuracy and Fairness for Juvenile Justice Risk Assessments. Journal of Empirical Legal Studies, 16(1): 175--194

work page 2019

[7] [7]

Brânzei, S.; Gkatzelis, V.; and Mehta, R. 2017. Nash Social Welfare Approximation for Strategic Agents. arXiv:1607.01569

work page Pith review arXiv 2017

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Budish, E. 2011. The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes. Journal of Political Economy, 119(6): 1061--1103

work page 2011