Research map / Learning theory and algorithms / Prediction and decision losses
Maximizing the Value of Predictions in Control: Accuracy Is Not Enough
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Introduces a stochastic framework for predictions in online control and defines "prediction power" as the optimal control-cost improvement from using predictions, giving a closed form for time-varying LQR and a lower bound for general nonlinear dynamics and costs.
Problem
Prior work bounds the benefit of predictions in control using prediction error (e.g., MSE or worst-case error bounds) and ignores the stochastic dependence between predictions and disturbances, so prediction accuracy is not a reliable proxy for control value.
Approach
Model predictions and disturbances jointly in a shared probability space, define prediction power as J*(baseline) minus J*(predictor) using optimal predictive policies, derive an exact closed form for LTV-LQR, and prove a general lower bound under two conditions (quadratic growth of the instance-dependent Q function and a covariance condition on the optimal action).
Key results
- In time-varying LQR, prediction power has a closed form P(theta)=sum_t Tr((R_t+B_t^T P_{t+1} B_t) E[Cov(u_t^theta | F_t(0))]); two predictors with identical per-entry MSE (Example 1, 2-D double integrator) yield significantly different control costs and prediction powers.
- A general lower bound P(theta) >= sum_t Tr(M_t Sigma_t) holds under two sufficient conditions (quadratic growth of the expected Q function and a covariance condition on the optimal action), with a trace-based variant using smallest eigenvalue of M_t.
- For LTV dynamics with strongly convex/smooth costs and jointly Gaussian weakly correlated predictions, P(theta) >= sum_t mu_u sigma_t, so even weak predictions (small lambda_t>0) yield strictly positive gains.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use exact predictions of each disturbance instead of an uninformative baseline | Online control with dynamics X_{t+1} = U_t + W_t and quadratic state costs · Toy control example | cost improvement: T | Helped |
| Change prediction structure while keeping the MSE for each disturbance entry the same | LTV LQR predictors V_t(θ) and V_t(I) · 2-D double-integrator LQR | control cost | Mixed |
| Use a predictor whose information is available one step earlier, with the same restricted policy class | M-GAPS · LQR online policy optimization | cost improvement | Hurt |
| Add predictions to the baseline controller | Optimal online control · General control setting | prediction power | No clear effect |
Surprising findings
- Predictors with identical per-entry MSE can have substantially different prediction power, so MSE is not a reliable proxy for control value.
- Prediction power can be unchanged across predictors with different information sets (1-D two-step example), while MSE differs.
Experimental setup
Metrics: prediction power MSE average control cost
Baselines: M-GAPS MPC with bounded prediction error optimal no-prediction policy
Builds on: prediction power (k-step perfect predictions) M-GAPS performance difference lemma model predictive control
Closest papers by meaning
- The Power of Predictions in Online Control (NeurIPS 2020 · similarity 0.92)
- Making Non-Stochastic Control (Almost) as Easy as Stochastic (NeurIPS 2020 · similarity 0.88)
- Disentangling Linear Quadratic Control with Untrusted ML Predictions (NeurIPS 2024 · similarity 0.85)
- Online Control with Adversarial Disturbance for Continuous-time Linear Systems (NeurIPS 2024 · similarity 0.85)
- Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator (ICLR 2025 · similarity 0.85)
- Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimization (ICML 2024 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.