---
title: "Beyond the Mean: Gaussian Distributional Successor Features for Zero-Shot Non-Linear Reward Adaptation"
authors:
  - "Yong Zhao"
  - "Wen Sun"
  - "Jianhua He"
  - "Peng Wang"
  - "Qubeijian Wang"
doi: "10.24963/ijcai.2026/601"
url: "https://ijcai.org/proceedings/2026/601"
pdf: "https://ijcai.org/proceedings/2026/0601.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "5396-5403"
track: "Main Track"
keywords:
  - "Machine Learning: Offline reinforcement learning"
  - "Machine Learning: Multi-task and transfer learning"
  - "Planning and Scheduling: Planning under uncertainty"
  - "Machine Learning: Model-based and model learning reinforcement learning"
  - "Machine Learning: Reinforcement learning"
---

# Beyond the Mean: Gaussian Distributional Successor Features for Zero-Shot Non-Linear Reward Adaptation

Yong Zhao, Wen Sun, Jianhua He, Peng Wang, Qubeijian Wang

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 5396-5403. DOI: [10.24963/ijcai.2026/601](https://doi.org/10.24963/ijcai.2026/601)

## Abstract

Zero-shot transfer for offline reinforcement learning involves generalizing to a wide range of tasks that are often risk-sensitive, without new interaction. We show here that although Successor Features (SFs) provide a principled framework for transfer through abstracting dynamics from rewards, their typical form is restricted to expected cumulative returns and is thus indifferent to variance in returns. We contend that such a mean-centric approach introduces bias by conflating risky and safe trajectories with identical expected outcomes, as it ignores outcome dispersion critical for risk-aware evaluation. Additionally, we note that distributional methods can be employed to model outcome distributions, but frequently do so at a high computational cost due to the need for discretization or elaborate sampling. To overcome this problem, we introduce a form of successor representation that incorporates an uncertainty envelope over states: Gaussian Distributional Successor Features (GDSF). Rather than inferring an implicit generative process, GDSF learns to approximate the distribution of cumulative outcomes with a Gaussian through recursive moment-matching. We present this framework for efficient representation of aleatoric uncertainty, without resorting to computationally expensive existing distributional methods. We also introduce Latent Outcome  Optimization, an inference procedure which finds high-reward outcomes in the data support and drives a goal-conditioned policy. This dual-mode design allows the agent to transfer to non-linear objectives in a zero-shot way while preserving closed-form efficiency for linear tasks. Experiments on the D4RL benchmark show that GDSF yields better performance in risk-sensitive tasks while achieving at least competitive results in standard linear regimes.