Pith. sign in

REVIEW 4 major objections 5 minor 27 references

A Hybrid Mean Field Framework for Aggregators Participating in Wholesale Electricity Markets

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A mean-field learning framework lets DER aggregators respond to endogenous electricity prices, and proves a unique equilibrium exists under a contraction condition, with Oahu simulations showing lower volatility and costs.

desk verdict A useful framework paper whose equilibrium theorem is conditional on constants the authors never compute, and whose numerical claims rest on thin statistical support; still worth refereeing. read the letter →

arxiv 2507.03240 v3 pith:AFK3RNTY submitted 2025-07-04 eess.SY cs.SY

Jun He , Andrew L. Liu This is my paper · ORCID
classification eess.SYcs.SY MSC 91A1690C40
keywords mean-fieldequilibriumreinforcementlearningwholesaleelectricitymarketlocationalmarginalpriceenergystoragedistributedresourcesvirtualpowerplantOahusystem
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 argues that a hybrid mean-field control / mean-field game framework, learned with a two-phase reinforcement-learning algorithm, enables many small solar-and-battery prosumers, coordinated by aggregators, to participate in wholesale electricity markets without treating prices as fixed. The central modeling move is to make locational marginal prices (LMPs) endogenous: aggregators act on LMPs, their collective storage actions change demand, and the revised LMPs feed back into the next decision round. The paper proves that under a Lipschitz contraction condition there is a unique mean-field equilibrium, and reports on a 37-bus Oahu case study that the learned policy reduces price volatility, lowers daily costs for both prosumers and consumers, and flattens the net demand curve. If correct, this is a scalable route to FERC Order 2222-style aggregator participation that does not require changing the ISO's market-clearing process.

What carries the argument

The central object is the mean-field equilibrium, defined as a fixed point of the consistency operator $\Gamma$ that updates the joint state-action distribution from the optimal policy, with LMPs derived from the economic dispatch dual variables and treated as a function of the mean field. Within each aggregator, a mean-field control formulation replaces the infinite prosumer population by a representative agent: the aggregator's policy maps storage level, net load, and hour of day to a charge/discharge action. Existence and uniqueness rest on a contraction-mapping argument (Theorem 3) whose condition is $L_1 L_{\mathrm{MF}} L_3 + L_2 < 1$, assembled from the Lipschitz continuity of LMPs in demand (Proposition 1, from the cited work), the Lipschitz continuity of the regularized optimal policy in the LMP profile, and the Lipschitz continuity of the consistency operator with respect to the mean field and policy. A regeneration probability $\zeta$ gives each prosumer a small chance of resetting to a uniformly sampled state, modeling prosumer turnover and keeping the environment dynamic at steady state.

What would settle it

Check the contraction condition numerically on the Oahu system: after training, estimate the four Lipschitz constants from the learned policy, the ED dual mapping, and the mean-field update; if $L_1 L_{\mathrm{MF}} L_3 + L_2 \ge 1$, the uniqueness theorem's hypothesis fails for the reported case. A second check is to run Algorithm 1 from several initial LMP beliefs and see whether the belief-update iteration (8) converges to the same fixed point; the paper explicitly leaves that convergence unproven.

Watch

Extended reading notes

Core claim

The central claim is that the infinite-population limit of many prosumers coordinated by a finite set of aggregators can be captured by a mean-field equilibrium: each aggregator's optimal storage policy is optimal given the aggregate state-action distribution, and that distribution is exactly the one induced when all aggregators follow those optimal policies. The paper proves existence and uniqueness of this equilibrium when the product of Lipschitz constants $L_1 L_{\mathrm{MF}} L_3 + L_2$ is strictly less than 1, where $L_1$ is the policy's Lipschitz constant in the LMP profile, $L_{\mathrm{MF}}$ is the LMP's Lipschitz constant in the mean field, and $L_2, L_3$ are the consistency operator's Lipschitz constants in the mean field and policy. A two-phase algorithm—offline RL training on a simulated environment with endogenous LMPs, then execution by broadcasting the learned stochastic policy to prosumers—approximates this equilibrium. On the Oahu system, the resulting MFE scenario yields significantly lower incremental mean volatility than a decentralized heuristic or a no-storage baseline, the lowest total daily costs for both prosumers and consumers, and the greatest load shifting, with charging during midday sunshine and reduced evening peaks.

Load-bearing premise

The load-bearing premise is that the contraction constant $L_1 L_{\mathrm{MF}} L_3 + L_2$ is actually less than 1 for the systems studied; the paper never computes or bounds these Lipschitz constants, so existence and uniqueness of the mean-field equilibrium remains an assumption rather than a checked fact for the Oahu case.

Editorial extensions

If this is right

  • Aggregators can remain price takers individually while the framework still captures price feedback, because LMPs carry the aggregate state-action distribution as a mean-field signal.
  • The framework is compatible with existing ISO operations: the economic dispatch problem is unchanged, and all learning and coordination happen at the aggregator level.
  • Coordinated storage control at scale lowers LMP volatility, as measured by incremental mean volatility, compared with a decentralized heuristic and a no-storage baseline.
  • Total daily costs fall for both prosumers and pure consumers, and the net demand profile is flattened, mitigating the duck curve.
  • The two-phase RL algorithm offers a scalable, decentralized approximation to the mean-field equilibrium in the infinite-agent limit, with convergence guaranteed when the contraction condition holds.

Reading between the lines

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

  • The contraction condition $L_1 L_{\mathrm{MF}} L_3 + L_2 < 1$ is checkable in practice: one could measure the four Lipschitz constants from the trained policy, the ED dual mapping, and the mean-field update during training, and use the condition as a stopping rule or to adjust the entropy-regularization strength to shrink $L_1$.
  • If the belief-update convergence question (explicitly left open in the paper) is resolved, the same hybrid MFC-MFE structure could extend to strategic aggregators who internalize their price impact, though the solution concept would need to become a game among aggregators rather than a competitive equilibrium.
  • The regeneration probability $\zeta$ controls how much exploration persists at steady state; varying it would test the robustness of the reported volatility and cost reductions to the assumed prosumer-turnover rate.
  • The numerical comparisons are scenario-based across five seeds; formal statistical tests on the IMV and cost differences would clarify whether the MFE advantage over DHA is significant beyond the shaded error bounds.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper develops a hybrid mean-field control (MFC) and mean-field game (MFG) framework for DER aggregators participating in wholesale electricity markets, with locational marginal prices (LMPs) determined endogenously through an economic dispatch problem. Each aggregator optimizes a large prosumer population by learning a storage policy, while aggregators interact indirectly through market clearing. The paper states conditions for existence and uniqueness of a mean-field equilibrium (MFE) in Appendix B, proposes a two-phase RL algorithm with LMP belief updates in Section V, and reports a case study on a 37-bus Oahu network in Section VI. The central theoretical claim is Theorem 3, which asserts a unique MFE following a 3-step fixed-point procedure under a contraction condition on Lipschitz constants; the numerical claim is that the MFE scenario yields lower volatility and costs than a heuristic benchmark or a no-storage baseline.

Significance. If the theoretical result were fully established and the numerics properly supported, the paper would offer a valuable step toward scalable, decentralized DER coordination with endogenous price feedback, an important problem in wholesale market design. The paper also makes a useful methodological contribution by combining MFC within an aggregator and MFG across aggregators, and by training policies with only observed LMPs. However, as it stands, the key existence/uniqueness theorem depends on unverified Lipschitz constants, the convergence of the actual RL algorithm is explicitly left to future work, and the numerical validation rests on only five seeds without significance testing. These issues affect the load-bearing claims of the paper, so the significance is not yet established at the level required for publication.

major comments (4)
  1. [Appendix B, Theorem 3] Theorem 3 asserts existence and uniqueness of an MFE under the condition L1 L_MF L3 + L2 < 1, but the paper never computes, bounds, or verifies L1, L_MF, L2, or L3 for the Oahu test system. With zeta = 0.01 in the numerical setup, Theorem 2's proof gives L2 = L3 = 1 - zeta = 0.99, so the condition reduces to L1 L_MF < 0.0101; no evidence is given that this holds, and given the per-bus storage capacity (about 8.5 MWh) and generator cost slopes up to 0.0342 $/MW^2h, the inequality is not obviously satisfied. The existence and uniqueness theorem therefore does not currently apply to the system used in the case study.
  2. [Appendix B, Theorem 3 proof] The proof of Theorem 3 conflates the scalar LMP lambda_t^n with the H-dimensional LMP profile lambda^n: Theorem 1's Lipschitz constant L1 is with respect to the profile (pi: S x R^H -> P(A)), whereas the displayed inequalities in the contraction argument use ||lambda_t^n - lambda_{t+H}^n||_1 as if these objects were interchangeable. The profile update occurs only at day boundaries, while the contraction comparison is made between time t and time t+H without defining a metric on profiles or connecting the pointwise LMP Lipschitz bound L_MF to the profile norm. This gap needs to be repaired for the contraction argument to be rigorous.
  3. [Section V, Algorithm 1; Section VII] Algorithm 1 trains policies under the LMP belief update (8), and the paper explicitly states in the conclusion that the belief-update dynamics and convergence of Algorithm 1 are left to future work and that the method is 'heuristic in practice.' Consequently, the claimed convergence of the learned policies to the unique MFE is not established for the algorithm actually simulated; the theoretical result covers only the idealized 3-step fixed-point procedure, not the belief-based RL algorithm deployed in the experiments.
  4. [Section VI] The numerical comparisons report five seeds per scenario with no significance tests and no confidence intervals beyond one-standard-deviation shadings; the claim that the MFE scenario 'yields significantly lower IMV' is therefore not statistically supported. No code or data release is mentioned, which limits reproducibility of the Oahu case study.
minor comments (5)
  1. [Section IV-A] The symbol lambda is used both for the scalar LMP lambda_t^n and for the H-vector profile lambda^n in Definition 1 and equation (7); please disambiguate, for example by writing lambda^n for the profile and lambda_t^n for the scalar.
  2. [Appendix B, Theorem 1] The strong-convexity parameter rho of the regularizer is never expressed in terms of the entropy coefficient alpha; since the negative entropy regularizer with coefficient alpha is rho-strongly convex with rho proportional to alpha, the Lipschitz constant L should be made explicit in terms of alpha.
  3. [Appendix B] The phrase 'all norms here are ℓ-norms' is incomplete; specify whether the norms are ℓ1, ℓ2, or ℓ∞, as the contraction argument uses an ℓ1 bound.
  4. [Figure 4 caption] The caption contains a garbled character ('/glyph1197et'); please fix the rendering.
  5. [Section III] The assumption that total net demand is nonnegative at each timestep is stated without justification; it would be helpful to cite a condition under which it holds or to note that it is a modeling simplification.

Circularity Check

0 steps flagged · score 1.0 of 10

No definitional circularity: the MFE existence/uniqueness claim is a conditional contraction argument, and the self-cited Lipschitz lemma is independent mathematical support; the main gaps are unverified contraction constants and an explicitly heuristic belief update, which are correctness concerns rather than circularity.

full rationale

The paper's central theoretical result, Theorem 3 in Appendix B, is a conditional statement: if the contraction constant L1*L_MF*L3 + L2 is strictly less than 1, then the 3-step fixed-point procedure has a unique fixed point, which is the MFE. This is a standard Banach fixed-point argument and does not define the MFE into existence or rename an input as a prediction. The Lipschitz constants are assumptions of the theorem, not fitted parameters, and the paper does not claim to verify them numerically; the fact that they are never computed for the Oahu system is a completeness and correctness limitation, not a circular step. Proposition 1, restated from the authors' prior work [13], is a parameter-free Lipschitz-continuity lemma with stated assumptions (LICQ and strongly convex quadratic costs) that do not include the target MFE result; under the review rules, such a citation counts as independent mathematical support even though the authors overlap, so it does not make the derivation circular. The numerical experiments are a self-contained simulation comparing MFE, DHA, and no-storage under the same endogenous price model; reporting lower prosumer costs under MFE is unsurprising because that cost is the optimized objective, but it is a benchmark comparison rather than a fitted-input-then-prediction construction. The paper explicitly admits in the Conclusion that Algorithm 1's LMP belief update makes the method 'heuristic in practice' and defers convergence analysis to future work; this is a real gap between the idealized 3-step theorem and the implemented algorithm, but it is an unsupported-convergence concern, not circular reasoning. Overall, no step in the derivation chain reduces by construction to its own inputs, so the circularity score is low.

Assumptions & free parameters 8 free parameters · 9 assumptions · 2 invented entities

The central claim rests on several hand-set numerical parameters, unverified Lipschitz and contraction assumptions, and two invented mechanisms (uniform regeneration and LMP beliefs) with no independent empirical support. The paper is a framework proposal: it contributes the architecture and a simulation, while the strongest theoretical guarantees remain conditional and mostly unchecked.

free parameters (8)
  • Regeneration probability zeta = 0.01
    Chosen for simulation; enters the mean-field update (7) and Lipschitz constants L2=L3=1-zeta in Theorem 2. No empirical calibration is provided.
  • LMP belief learning rate delta_n = 0.9
    Hand-set in belief update (8); convergence of this update is not proved, and the value is not varied in sensitivity analysis.
  • Entropy regularization strength alpha = not reported
    Controls exploration in the regularized reward (5) and appears in the policy Lipschitz constant L via the 1/rho smoothness of the Fenchel conjugate; no value or sensitivity is given.
  • Discount factor gamma_n = not reported
    Determines the value function (6) and inflates the Lipschitz constant by 1/(1-gamma); no value is reported.
  • Storage capacity and type mix E_n, theta_n^k, b_n^k = 10/20/30 kWh; 500/100/50 prosumers; relative weights unspecified
    Case-study configuration from [26] and assumptions; not fitted to measured DER data.
  • DHA thresholds lambda_low, lambda_high and randomization alpha = thresholds not reported; alpha=0.8
    Benchmark parameters; poor choice affects the comparison, and no sensitivity analysis is provided.
  • Triangular noise parameters = Delta(0.8,1.2,1) solar, Delta(0.5,1.5,1) wind
    Uncertainty model added for the case study; not calibrated to forecast error data.
  • Training length T_train and day length H = T_train=1200, H=12
    PPO training budget and discretization; chosen by hand with no ablation.
assumptions (9)
  • domain assumption LICQ holds at every feasible point of the economic dispatch problem for all demand vectors (Assumption 1).
    Needed for Proposition 1 that LMPs are single-valued and Lipschitz; not verified for the Oahu network or for all sampled demand realizations.
  • domain assumption Generator cost functions are strongly convex and quadratic (Proposition 1).
    The synthetic Oahu data uses quadratic oil/biomass costs and zero-cost renewables, so the assumption is plausible for the case study but not guaranteed for real markets.
  • domain assumption State and action spaces S and A are discrete and finite.
    Stated in Section IV-A before defining the mean field; needed for the histogram definition and Gamma update, but the numerical model uses continuous battery levels discretized implicitly by PPO.
  • domain assumption Total net demand across all buses is non-negative at each time t.
    Stated in Section III to avoid infeasible supply-demand imbalance; may fail under high solar penetration in real systems.
  • domain assumption Aggregators are non-strategic price takers.
    Section IV-A; this contradicts the abstract's claim that the MFG models strategic interactions among aggregators and limits the game-theoretic scope to competitive equilibrium.
  • domain assumption The infinite-population mean-field limit is a valid approximation of finite prosumer populations without an error bound.
    Section IV; the paper explicitly defers the connection to finite-M Nash equilibria to future work, citing [18].
  • ad hoc to paper The contraction constant condition L1 L_MF L3 + L2 < 1 holds for the system.
    Theorem 3's existence and uniqueness conclusion depends on this bound, but no constants are estimated and the condition is not tested in the case study.
  • ad hoc to paper The LMP belief update (8) tracks the true price profile well enough for policy training.
    The algorithm assumes this, but the paper's future-work section admits belief-update convergence is unproven and Algorithm 1 is heuristic.
  • domain assumption The regeneration probability zeta models prosumer turnover.
    Introduced in Section IV-B and used in both the consistency operator and the simulated state transition (9); no empirical basis and it strongly affects the contraction proof via L2=L3=1-zeta.
invented entities (2)
  • Uniform regeneration mechanism with probability zeta
    purpose: Resets each prosumer's state to a uniformly sampled state, representing customer turnover and preventing the mean field from freezing; used in the consistency operator Gamma (7) and simulated transitions (9).
    There is no data support for a uniform reset distribution. It is a modeling device that directly sets L2=L3=1-zeta and therefore determines the contraction bound in Theorem 3.
  • LMP belief vector lambda_hat_t^n
    purpose: Each aggregator maintains a daily price profile belief used for policy training in Phase 1 and updated by (8); it replaces direct knowledge of the mean field.
    An algorithmic construct introduced by the authors. Its convergence is not proved, and the paper relies on it for the two-phase learning loop.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Hybrid Mean Field Framework for Aggregators Participating in Wholesale Electricity Markets." pith.science (2026). https://pith.science/paper/AFK3RNTY

@misc{pith2026250703240,
  author       = {Pith},
  title        = {Pith review of: A Hybrid Mean Field Framework for Aggregators Participating in Wholesale Electricity Markets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AFK3RNTY}},
  note         = {Machine review of arXiv:2507.03240}
}
read the original abstract

The rapid growth of distributed energy resources (DERs), including rooftop solar and energy storage, is transforming the grid edge, where distributed technologies and customer-side systems increasingly interact with the broader power grid. DER aggregators, entities that coordinate and optimize the actions of many small-scale DERs, play a key role in this transformation. This paper presents a hybrid Mean-Field Control (MFC) and Mean-Field Game (MFG) framework for integrating DER aggregators into wholesale electricity markets. Unlike traditional approaches that treat market prices as exogenous, our model captures the feedback between aggregators' strategies and locational marginal prices (LMPs) of electricity. The MFC component optimizes DER operations within each aggregator, while the MFG models strategic interactions among multiple aggregators. To account for various uncertainties, we incorporate reinforcement learning (RL), which allows aggregators to learn optimal bidding strategies in dynamic market conditions. We prove the existence and uniqueness of a mean-field equilibrium and validate the framework through a case study of the Oahu Island power system. Results show that our approach reduces price volatility and improves market efficiency, offering a scalable and decentralized solution for DER integration in wholesale markets.

Figures

Figures reproduced from arXiv: 2507.03240 by the authors.

Figure 3
Figure 3. Comparison of daily costs for prosumers and consumers. Shaded [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Comparison of net load curves. VII. CONCLUSION This paper develops an algorithmic framework for integrating DERs into wholesale electricity markets through decentralized, RL-enabled aggregators. Aggregators learn storage charging and discharging strategies for prosumers under uncertainty in renewable output, demand, and market prices. A central idea is to treat LMPs as a mean-field signal that reflects aggregate sup… view at source ↗
Figure 2
Figure 2. Comparison of IMV over the last 3 days across scenarios. Shaded [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 24 canonical work pages

  1. [13]

    Decentralized Integration of Grid Edge Resources into Wholesale Electricity Markets via Mean-field Games

    C. Feng and A. L. Liu, “Decentralized integration of grid edge resources into wholesale electricity markets via mean-field games,” arXiv preprint arXiv:2503.07984, 2025

    work page Pith review arXiv 2025

  2. [1]

    OhmConnect paid members $2.7M and saved 1.5 GWh of energy during recent California heat wave,

    OhmConnect, “OhmConnect paid members $2.7M and saved 1.5 GWh of energy during recent California heat wave,” October 2022. Accessed: 2025-06-23

    work page 2022

  3. [2]

    Tesla virtual power plant,

    Tesla, Inc., “Tesla virtual power plant,” June 2025. Accessed: 2025-06- 23

    work page 2025

  4. [3]

    Partic- ipation of an energy storage aggregator in electricity markets,

    J. E. Contreras-Ocana, M. A. Ortega-Vazquez, and B. Zhang, “Partic- ipation of an energy storage aggregator in electricity markets,” IEEE Transactions on Smart Grid, vol. 10, no. 2, pp. 1171–1183, 2017

    work page 2017

  5. [4]

    On efficient aggregation of dis- tributed energy resources,

    Z. Gao, K. Alshehri, and J. R. Birge, “On efficient aggregation of dis- tributed energy resources,” in 2021 60th IEEE Conference on Decision and Control (CDC), pp. 7064–7069, IEEE, 2021

    work page 2021

  6. [5]

    Robust bidding strategy for ag- gregation of distributed prosumers in flexiramp market,

    M. Khoshjahan and M. Kezunovic, “Robust bidding strategy for ag- gregation of distributed prosumers in flexiramp market,” Electric Power Systems Research, vol. 209, p. 107994, 2022

    work page 2022

  7. [6]

    Optimal bidding strategy for an aggregator of prosumers in energy and secondary reserve markets,

    J. Iria, F. Soares, and M. Matos, “Optimal bidding strategy for an aggregator of prosumers in energy and secondary reserve markets,” Applied Energy, vol. 238, pp. 1361–1372, 2019

    2019

  8. [7]

    Deep reinforcement learning for strategic bidding in electricity markets,

    Y . Ye, D. Qiu, M. Sun, D. Papadaskalopoulos, and G. Strbac, “Deep reinforcement learning for strategic bidding in electricity markets,” IEEE Transactions on Smart Grid, vol. 11, no. 2, pp. 1343–1355, 2020

    work page 2020

Show all 27 references
  1. [8]

    Linear programming for multi-agent demand response,

    A. Fallahi, J. M. Rosenberger, V . C. Chen, W.-J. Lee, and S. Wang, “Linear programming for multi-agent demand response,” IEEE Access, vol. 7, pp. 181479–181490, 2019

    2019

  2. [9]

    A stochastic multi-layer agent- based model to study electricity market participants behavior,

    M. Shafie-khah and J. P. Catal ˜ao, “A stochastic multi-layer agent- based model to study electricity market participants behavior,” IEEE Transactions on Power Systems, vol. 30, no. 2, pp. 867–881, 2014

    2014

  3. [10]

    Wholesale market partic- ipation of DERAs: DSO-DERA-ISO coordination,

    C. Chen, S. Bose, T. D. Mount, and L. Tong, “Wholesale market partic- ipation of DERAs: DSO-DERA-ISO coordination,” IEEE Transactions on Power Systems, 2024

    2024

  4. [11]

    Multi-agent learning in repeated double-side auctions for peer-to-peer energy trading,

    A. Liu and Z. Zhao, “Multi-agent learning in repeated double-side auctions for peer-to-peer energy trading,” in Proceedings of the 54th Hawaii International Conference on System Sciences, p. 3121, 2021

    2021

  5. [12]

    Multi-agent reinforcement learn- ing: A selective overview of theories and algorithms,

    K. Zhang, Z. Yang, and T. Bas ¸ar, “Multi-agent reinforcement learn- ing: A selective overview of theories and algorithms,” Handbook of reinforcement learning and control, pp. 321–384, 2021

    2021

  6. [14]

    Learning mean-field games,

    X. Guo, A. Hu, R. Xu, and J. Zhang, “Learning mean-field games,” Advances in neural information processing systems, vol. 32, 2019

    2019

  7. [15]

    Learning while playing in mean-field games: Convergence and optimality,

    Q. Xie, Z. Yang, Z. Wang, and A. Minca, “Learning while playing in mean-field games: Convergence and optimality,” in Proceedings of the 38th International Conference on Machine Learning (M. Meila and T. Zhang, eds.), vol. 139 of Proceedings of Machine Learning Research, pp. 11...

    2021

  8. [16]

    Oracle-free reinforcement learning in mean-field games along a single sample path,

    M. A. U. Zaman, A. Koppel, S. Bhatt, and T. Basar, “Oracle-free reinforcement learning in mean-field games along a single sample path,” in Proceedings of The 26th International Conference on Artificial Intelligence and Statistics (F. Ruiz, J. Dy, and J.-W. van de Meent, eds.),...

    2023

  9. [17]

    Mean-field control based approximation of multi-agent reinforcement learning in presence of a non-decomposable shared global state,

    W. U. Mondal, V . Aggarwal, and S. Ukkusuri, “Mean-field control based approximation of multi-agent reinforcement learning in presence of a non-decomposable shared global state,” Transactions on Machine Learning Research, 2023

    2023

  10. [18]

    Markov-Nash equilibria in mean-field games with discounted cost,

    N. Saldi, T. Basar, and M. Raginsky, “Markov-Nash equilibria in mean-field games with discounted cost,” SIAM Journal on Control and Optimization, vol. 56, no. 6, pp. 4256–4287, 2018

    2018

  11. [19]

    Peer-to-peer energy trading of solar and energy storage: A networked multiagent reinforcement learning approach,

    C. Feng and A. L. Liu, “Peer-to-peer energy trading of solar and energy storage: A networked multiagent reinforcement learning approach,” Applied Energy, vol. 383, p. 125283, 2025

    2025

  12. [20]

    Grid structural characteristics as validation criteria for synthetic net- works,

    A. B. Birchfield, T. Xu, K. M. Gegner, K. S. Shetye, and T. J. Overbye, “Grid structural characteristics as validation criteria for synthetic net- works,” IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 3258– 3265, 2017

    2017

  13. [21]

    Power facts,

    Hawaiian Electric, “Power facts,” 3 2024

    2024

  14. [22]

    An 8-zone test system based on ISO New England data: Development and application,

    D. Krishnamurthy, W. Li, and L. Tesfatsion, “An 8-zone test system based on ISO New England data: Development and application,” IEEE Transactions on Power Systems, vol. 31, no. 1, pp. 234–246, 2016

    2016

  15. [23]

    Cost and per- formance assumptions for modeling electricity generation technologies,

    R. Tidball, J. Bluestein, N. Rodriguez, and S. Knoke, “Cost and per- formance assumptions for modeling electricity generation technologies,” tech. rep., National Renewable Energy Lab.(NREL), Golden, CO (United States), 2010

    2010

  16. [24]

    Solar PV Analysis of Honolulu, United States,

    A. Robinson, “Solar PV Analysis of Honolulu, United States,” 2024

    2024

  17. [25]

    Wind power characteristics of oahu, hawaii,

    D. Arg ¨ueso and S. Businger, “Wind power characteristics of oahu, hawaii,” Renewable Energy, vol. 128, pp. 324–336, 2018

    2018

  18. [26]

    Estimating the opportunity for load-shifting in Hawaii

    M. Coffman, P. Bernstein, S. Wee, and A. Arik, “Estimating the opportunity for load-shifting in Hawaii.” https://uhero.hawaii.edu/R ePEc/hae/wpaper/WP 2016-10.pdf, 2016

    2016

  19. [27]

    V olatility of power grids under real-time pricing,

    M. Roozbehani, M. A. Dahleh, and S. K. Mitter, “V olatility of power grids under real-time pricing,” IEEE Transactions on Power Systems, vol. 27, no. 4, pp. 1926–1940, 2012

    1926

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.