Causal Matrix Completion: Applications to Offline Causal Reinforcement Learning

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" summary

Proposes a practical algorithm called synthetic nearest neighbors that combines nearest neighbors and synthetic controls to handle MNAR matrix completion, proves entry-wise consistency and asymptotic normality, and shows it recovers an 80×80 rank‑5 distribution where USVT and SoftImpute break down. Requires a low‑rank latent factor model with selection on latent factors, gives a sample‑efficient experimental design (recover M×N from ~M+N budget; cost ~M K^2+N K^3), and extends to causal tensor completion for offline RL (PER‑SIM learns latent mass and outperforms CADM in MountainCar/HalfCheetah).

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" chapters (27)

1. 0:00Intro
2. 1:21Recommendation systems
3. 2:59Contextual bandits
4. 4:35Formal setup for matrix completion
5. 5:37Models for missingness
6. 6:39MCAR & L-MNAR: not a unified approach to sparsity patterns of interest
7. 9:07Does the sparsity pattern matter? An empirical example
8. 10:35Missing completely at random (MCAR) data
9. 12:25"Limited"-missing not at random (L-MNAR) data
10. 13:10Missing not at random (MNAR) data
11. 15:44Synthetic controls (SC)
12. 22:51What type of missing is allowed?-selection on latent factors
13. 24:12Other operating assumptions
14. 27:16Theoretical results for SNN
15. 28:30Simplifying assumption
16. 31:33Experiment design: a motivating example from drug design
17. 31:56Experiment design: a matrix completion perspective
18. 33:18Experiment design: "optimal" observation pattern
19. 35:26Towards heteroskedastic variance estimation
20. 36:32Heteroskedastic variance estimation algorithm
21. 37:19Statistical guarantees
22. 38:32An important connection
23. 39:23What is behind some of the most popular RL achievements?
24. 40:16Simulators are abundant in core engineering systems too
25. 41:41PerSim: a motivating example
26. 42:18Heterogenous Agents Need Different Policies
27. 43:36PerSim: a tensor completion perspective

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