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Performative Control for Linear Dynamical Systems
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Introduces performative control for linear dynamical systems, where the chosen disturbance-action policy shifts the state-transition dynamics; gives conditions for a unique performatively stable control solution and a repeated SGD scheme converging at O(1/N).
Problem
Control of linear dynamical systems whose state transition dynamics change in response to the deployed control policy, producing policy-dependent temporal correlations that existing performative prediction and static LDS control frameworks do not handle.
Approach
Extends performative prediction to control: the policy-dependent state transition perturbations form a time-varying sensitivity structure, and a sufficient condition on weighted sums of distributional sensitivities (propagated and aggregated over the horizon) guarantees a unique performatively stable control (PSC) solution; disturbance-action policies enable convex costs; stability regimes give di
Key results
- Under almost surely strongly stable dynamics, the PS error decays at O(1/N) for all three sensitivity orderings (descending, ascending, random), consistent with theory.
- Under almost surely unstable dynamics, iterates diverge for descending and random sensitivity sequences, while ascending sequence converges, matching the backward-decay requirement.
- RSGD converges to the PSC solution with expected squared distance decaying as O(1/N) under the sufficient condition.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ascending rather than descending or random sensitivity order under almost surely unstable dynamics | RSGD for stock investment risk minimization · Stock investment simulation, almost surely unstable dynamics | expected total control cost | Helped |
| Reorder the same sensitivities under almost surely strongly stable dynamics | RSGD for stock investment risk minimization · Stock investment simulation, almost surely strongly stable dynamics | PS error | No clear effect |
| Use descending or random sensitivity order instead of ascending under almost surely unstable dynamics | RSGD for stock investment risk minimization · Stock investment simulation, almost surely unstable dynamics | PS error | Hurt |
| Vary the sensitivity order among ascending, descending, and random under general dynamics | RSGD for stock investment risk minimization · Stock investment simulation, general dynamics | PS error | No clear effect |
| Use RSGD with the three tested sensitivity patterns under almost surely strongly stable dynamics | RSGD for stock investment risk minimization · Stock investment simulation, almost surely strongly stable dynamics | PS error | Helped |
Surprising findings
- For almost surely unstable dynamics, large early-time sensitivities rule out existence of the PSC solution, so sensitivities must decay backward in time.
Limitations
- Only the state transition matrix is performative; control input gain B and noise are non-performative.
- Restricted to linear dynamics and disturbance-action policies; general nonlinear or general control costs left to future work.
- Experiments limited to a single simulated stock investment example.
Experimental setup
Datasets: simulated stock market returns under stochastic volatility model
Benchmarks: simulated stock investment risk minimization (L=10 stocks, T=60 days)
Metrics: performative stable error ||M_N - M_PS||_F^2 expected total control cost
Baselines: performative optimal control (POC)
Builds on: performative prediction stateful performative prediction non-stochastic control disturbance-action policy
Closest papers by meaning
- Performative Reinforcement Learning (ICML 2023 · similarity 0.88)
- Performative Policy Gradient: Optimality in Performative Reinforcement Learning (ICML 2026 · similarity 0.88)
- Stabilizing Dynamical Systems via Policy Gradient Methods (NeurIPS 2021 · similarity 0.88)
- Learning Control-Oriented Dynamical Structure from Data (ICML 2023 · similarity 0.86)
- Stochastic Optimization Schemes for Performative Prediction with Nonconvex Loss (NeurIPS 2024 · similarity 0.84)
- The Stability of Online Algorithms in Performative Prediction (NeurIPS 2026 · similarity 0.83)
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