Strategic Federated Learning: Application to Smart Meter Data Clustering

TL;DR

This work addresses the misalignment between the fusion center's (FC) objectives and client incentives in federated learning (FL) by introducing strategic federated learning (SFL), where clients influence FC decisions only through reporting noisy model information and may inject strategic noise $\boldsymbol{Z}_m$ into their MI. The proposed approach provides a general framework for strategic information transmission, renders the FC's decision problem as a function of aggregated MI $\widehat{\boldsymbol{R}}_{\boldsymbol{Z}}$ (with $\widehat{\underline{g}} = \Gamma_{\widehat{\boldsymbol{R}}_{\boldsymbol{Z}}}(\underline{g})$), and mixes a common FC utility with each client's private utility via $U(\underline{x};\widehat{\underline{g}}) = u(\underline{x}; \widehat{\underline{g}}) + \sum_m \alpha_m u_m(\underline{x}_m; \widehat{\underline{g}}_m)$. The framework is specialized to clustering for smart-meter data and applied to power consumption scheduling, using Ausgrid data to demonstrate how strategic noise can reduce a client's costs and induce Nash equilibria with bounded inefficiency. Numerical results in 2D show substantial client gains from appropriately chosen mean noise, while higher-dimensional experiments (48D) confirm NE behavior with meaningful but smaller gains, illustrating the practical impact of strategic MI reporting on energy management and the potential need for incentives or new defense mechanisms in FL systems.

Abstract

Federated learning (FL) involves several clients that share with a fusion center (FC), the model each client has trained with its own data. Conventional FL, which can be interpreted as an estimation or distortion-based approach, ignores the final use of model information (MI) by the FC and the other clients. In this paper, we introduce a novel FL framework in which the FC uses an aggregate version of the MI to make decisions that affect the client's utility functions. Clients cannot choose the decisions and can only use the MI reported to the FC to maximize their utility. Depending on the alignment between the client and FC utilities, the client may have an individual interest in adding strategic noise to the model. This general framework is stated and specialized to the case of clustering, in which noisy cluster representative information is reported. This is applied to the problem of power consumption scheduling. In this context, utility non-alignment occurs, for instance, when the client wants to consume when the price of electricity is low, whereas the FC wants the consumption to occur when the total power is the lowest. This is illustrated with aggregated real data from Ausgrid \cite{ausgrid}. Our numerical analysis clearly shows that the client can increase his utility by adding noise to the model reported to the FC. Corresponding results and source codes can be downloaded from \cite{source-code}.

Figures (4)

• Figure 1: Description of the general strategic federated learning (SFL) framework. Based on a given aggregate model information knowledge $\widehat{\boldsymbol{R}}_{\boldsymbol{Z}}$, the fusion center takes decisions $\underline{x} =(\underline{x}_1,...,\underline{x}_M)$ which maximizes its utility function $U$ and affect the clients' utility functions $\overline{u}_1,...\overline{u}_M$. The vector $\underline{g}$ represents the system state (e.g., the forecast of non-controllable consumption power or the radio channel state), and $\Gamma_{\widehat{\boldsymbol{R}}_{\boldsymbol{Z}}}(\underline{g})$ is the knowledge about the state through the learning model/function $\Gamma$. Client $m$ can influence the fusion center only through the model information reported $\widehat{\boldsymbol{R}}_m$, hence the presence of a strategic noise $\boldsymbol{Z}_m$.
• Figure 2: A single client is assumed. (a) It is seen that the client can reduce its cost from $5.34$ (when reporting its model perfectly to the fusion center, which is indicated by the black arrow) to $0.73$ by adding noise to the model reported to the fusion center, the optimal mean of the Gaussian noise being $\underline{\mu}_1=(2.650, -2.359)$. (b) The zero-noise point is Pareto dominated by the South-West orthant, which shows that the client can benefit from the noised model. Generally, most of the benefits of adding noise to the model are for the client who can make his cost as low as 0.73. However, adding a large negative noise vector to the model results in $\Gamma_{\widehat{\boldsymbol{R}}_{\boldsymbol{Z}}}(\underline{g}) = 0$ due to clipping negative values in client's model, decreasing the fusion center's cost.
• Figure 3: Two clients are assumed. Expected costs for Clients 1 and 2 w.r.t $\underline{\mu}_1(1)$, $\underline{\mu}_2(1)$ with 2D data. Potential Nash equilibrium (NE) points are marked at $(1.456, 2.223), (1.824, 1.581)$, and $(2.837, 0.405)$. At the NE points, the costs are much lower than at the point where the model is perfectly revealed to the fusion center.
• Figure 4: Two clients are assumed. Expected costs for Clients 1 and 2 w.r.t. $\lambda_1$, $\lambda_2$ in the 48-dimensional data case. Nash equilibrium points: $(4.204, 4.401)$, $(4.368, 4.335)$, $(4.5, 4.434)$. Costs at these points are lower than at the point with perfect model revelation to the fusion center, though the gain is less significant than in the 2D data case.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4