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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.10790 |
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| _version_ | 1866910830595932160 |
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| author | Ollivier, Yann |
| author_facet | Ollivier, Yann |
| contents | In reinforcement learning, universal successor features (SFs) are a way to provide zero-shot adaptation to new tasks at test time: they provide optimal policies for all downstream reward functions lying in the linear span of a set of base features. But it is unclear what constitutes a good set of base features, that could be useful for a wide set of downstream tasks beyond their linear span. Laplacian eigenfunctions (the eigenfunctions of $Δ+Δ^\ast$ with $Δ$ the Laplacian operator of some reference policy and $Δ^\ast$ that of the time-reversed dynamics) have been argued to play a role, and offer good empirical performance.
Here, for the first time, we identify the optimal base features based on an objective criterion of downstream performance, in a non-tautological way without assuming the downstream tasks are linear in the features. We do this for three generic classes of downstream tasks: reaching a random goal state, dense random Gaussian rewards, and random ``scattered'' sparse rewards. The features yielding optimal expected downstream performance turn out to be the \emph{same} for these three task families. They do not coincide with Laplacian eigenfunctions in general, though they can be expressed from $Δ$: in the simplest case (deterministic environment and decay factor $γ$ close to $1$), they are the eigenfunctions of $Δ^{-1}+(Δ^{-1})^\ast$.
We obtain these results under an assumption of large behavior cloning regularization with respect to a reference policy, a setting often used for offline RL. Along the way, we get new insights into KL-regularized\option{natural} policy gradient, and into the lack of SF information in the norm of Bellman gaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Which Features are Best for Successor Features? Ollivier, Yann Machine Learning Optimization and Control In reinforcement learning, universal successor features (SFs) are a way to provide zero-shot adaptation to new tasks at test time: they provide optimal policies for all downstream reward functions lying in the linear span of a set of base features. But it is unclear what constitutes a good set of base features, that could be useful for a wide set of downstream tasks beyond their linear span. Laplacian eigenfunctions (the eigenfunctions of $Δ+Δ^\ast$ with $Δ$ the Laplacian operator of some reference policy and $Δ^\ast$ that of the time-reversed dynamics) have been argued to play a role, and offer good empirical performance. Here, for the first time, we identify the optimal base features based on an objective criterion of downstream performance, in a non-tautological way without assuming the downstream tasks are linear in the features. We do this for three generic classes of downstream tasks: reaching a random goal state, dense random Gaussian rewards, and random ``scattered'' sparse rewards. The features yielding optimal expected downstream performance turn out to be the \emph{same} for these three task families. They do not coincide with Laplacian eigenfunctions in general, though they can be expressed from $Δ$: in the simplest case (deterministic environment and decay factor $γ$ close to $1$), they are the eigenfunctions of $Δ^{-1}+(Δ^{-1})^\ast$. We obtain these results under an assumption of large behavior cloning regularization with respect to a reference policy, a setting often used for offline RL. Along the way, we get new insights into KL-regularized\option{natural} policy gradient, and into the lack of SF information in the norm of Bellman gaps. |
| title | Which Features are Best for Successor Features? |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2502.10790 |