A Framework for Designing Reward Functions: From Objectives to Feature-Based Reward Design

Forum topic · 小凯 · 2026-08-14

Summary

This arXiv paper (2508.03415) by Di Yang Shi and W. Bradley Knox presents a formal process that enables non-experts to instantiate and iterate on human-aligned reward functions, i.e., reward functions consistent with a given preference ranking over trajectories. Given a natural-language task description, the pipeline produces a linear reward function in three steps: (1) a guided workflow for distilling task objectives into a set of fundamental objectives and deriving measurable outcome variables capturing them; (2) selecting a causally representative subset of outcome variables as reward terms, formulated as a minimum-cost partial cover problem on a causal DAG solvable in polynomial time via max-flow; and (3) fitting weights for the reward terms as a convex feasibility problem, iteratively tightened through preference queries and solved with existing separation-oracle methods. Notably, the authors claim this is the first reward design method that preserves a deterministic conflict-free feasible weight region, contracting to a desired tolerance within O(n log kappa) preference queries via a separation oracle. The work is relevant to reinforcement learning, reward design, and human-in-the-loop preference learning.

Paper Overview

Field: Machine Learning Authors: Di Yang Shi, W. Bradley Knox Published: 2026-08-13 arXiv: 2508.03415

Abstract

This paper presents a formal process that enables non-experts to instantiate and iterate on human-aligned reward functions — reward functions that are consistent with a given preference ranking over trajectories.

Given a natural-language description of a task, the pipeline produces a linear reward function through three steps:

1. Objectives to outcome variables: Distill the task objectives into a set of fundamental objectives, and derive measurable outcome variables that capture these fundamental objectives. The paper's contribution for this step is a guided workflow for deriving the outcome variables.

2. Reward term selection: Choose a causally representative subset of the outcome variables as reward terms. This is reduced to a minimum-cost partial cover problem on a causal DAG, which is solvable in polynomial time via max-flow.

3. Weight fitting: Fit weights for the reward terms by framing the task as a convex feasibility problem that is iteratively tightened through preference queries, solved with existing separation-oracle methods.

Key Contribution

To the authors' knowledge, this is the first reward design method that preserves a deterministic conflict-free feasible weight region, contracting to a desired tolerance within O(n log κ) preference queries via a separation oracle.

Significance

The framework lowers the barrier for non-experts to specify rewards that are aligned with human preferences, connecting natural-language task descriptions, causal reasoning over outcome variables, and efficient query-based weight fitting.

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