Formalizing Task-Space Complexity for Zero-Shot Generalization

Jung-Hoon Cho, Heling Zhang, Siqi Du, Roy Dong, Cathy Wu
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1212-1228, 2026.

Abstract

Policies must operate across diverse conditions, yet a single policy is often conservative while fully adaptive schemes can be complex. We study zero-shot generalization in contextual dynamical systems and introduce a performance-centric, directional task dissimilarity—the signed divergence—that upper bounds the generalization gap from a source context to a target context. The signed divergence induces $\varepsilon$-tolerance sets that certify when a source policy class generalizes, and it yields a concrete notion of task-space complexity: the minimum number of source contexts needed so that every target context incurs at most $\varepsilon$ generalization gap. Under a mild local smoothness assumption on performance, the induced tolerance sets admit certified inner/outer balls and instance-dependent volume bounds on task-space complexity. In the finite-oracle setting, source selection reduces to set cover; a greedy strategy inherits the standard $H(n)$ approximation guarantee. Using a Mass-Spring-Damper system with linear–quadratic regulator (LQR) controllers and a nonlinear CartPole system with deep reinforcement learning controllers, we show that greedy selection achieves the same $\varepsilon$-coverage with fewer policies than uniform or random baselines. Our approach delivers a performance-based task similarity measure and practical certificates for building generalizable control with simple policies.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-cho26a, title = {Formalizing Task-Space Complexity for Zero-Shot Generalization}, author = {Cho, Jung-Hoon and Zhang, Heling and Du, Siqi and Dong, Roy and Wu, Cathy}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1212--1228}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/cho26a/cho26a.pdf}, url = {https://proceedings.mlr.press/v331/cho26a.html}, abstract = {Policies must operate across diverse conditions, yet a single policy is often conservative while fully adaptive schemes can be complex. We study zero-shot generalization in contextual dynamical systems and introduce a performance-centric, directional task dissimilarity—the signed divergence—that upper bounds the generalization gap from a source context to a target context. The signed divergence induces $\varepsilon$-tolerance sets that certify when a source policy class generalizes, and it yields a concrete notion of task-space complexity: the minimum number of source contexts needed so that every target context incurs at most $\varepsilon$ generalization gap. Under a mild local smoothness assumption on performance, the induced tolerance sets admit certified inner/outer balls and instance-dependent volume bounds on task-space complexity. In the finite-oracle setting, source selection reduces to set cover; a greedy strategy inherits the standard $H(n)$ approximation guarantee. Using a Mass-Spring-Damper system with linear–quadratic regulator (LQR) controllers and a nonlinear CartPole system with deep reinforcement learning controllers, we show that greedy selection achieves the same $\varepsilon$-coverage with fewer policies than uniform or random baselines. Our approach delivers a performance-based task similarity measure and practical certificates for building generalizable control with simple policies.} }
Endnote
%0 Conference Paper %T Formalizing Task-Space Complexity for Zero-Shot Generalization %A Jung-Hoon Cho %A Heling Zhang %A Siqi Du %A Roy Dong %A Cathy Wu %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-cho26a %I PMLR %P 1212--1228 %U https://proceedings.mlr.press/v331/cho26a.html %V 331 %X Policies must operate across diverse conditions, yet a single policy is often conservative while fully adaptive schemes can be complex. We study zero-shot generalization in contextual dynamical systems and introduce a performance-centric, directional task dissimilarity—the signed divergence—that upper bounds the generalization gap from a source context to a target context. The signed divergence induces $\varepsilon$-tolerance sets that certify when a source policy class generalizes, and it yields a concrete notion of task-space complexity: the minimum number of source contexts needed so that every target context incurs at most $\varepsilon$ generalization gap. Under a mild local smoothness assumption on performance, the induced tolerance sets admit certified inner/outer balls and instance-dependent volume bounds on task-space complexity. In the finite-oracle setting, source selection reduces to set cover; a greedy strategy inherits the standard $H(n)$ approximation guarantee. Using a Mass-Spring-Damper system with linear–quadratic regulator (LQR) controllers and a nonlinear CartPole system with deep reinforcement learning controllers, we show that greedy selection achieves the same $\varepsilon$-coverage with fewer policies than uniform or random baselines. Our approach delivers a performance-based task similarity measure and practical certificates for building generalizable control with simple policies.
APA
Cho, J., Zhang, H., Du, S., Dong, R. & Wu, C.. (2026). Formalizing Task-Space Complexity for Zero-Shot Generalization. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1212-1228 Available from https://proceedings.mlr.press/v331/cho26a.html.

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