A Framework for Designing Reward Functions from Objectives to Feature Weights

Forum topic · 小凯 · 2026-08-14

Summary

This paper introduces a formal three-step framework that allows non-experts to instantiate and iteratively refine human-aligned reward functions from natural-language task descriptions. Step 1 guides users to distill task objectives into measurable outcome variables. Step 2 reduces reward-term selection to a minimum-cost partial cover problem on a causal DAG, solvable in polynomial time via max-flow. Step 3 casts weight fitting as a convex feasibility problem, iteratively shrinking the feasible weight region via preference queries solved by a separating-oracle method. The authors claim this is the first reward-design approach that preserves a deterministic, conflict-free feasible weight region, converging to a desired tolerance in O(n log κ) preference queries. The contribution details Step 1 as a guided workflow and formalizes Steps 2 and 3.

Paper Overview

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

Abstract (English)

We present a formal process to enable non-experts to instantiate and iterate on human-aligned reward functions—that is, reward functions that respect a given ranking of trajectory preferences. Given a natural-language description of a task, this process produces a linear reward function through three steps:

1. Distill the task objectives into a set of base objectives and derive measurable outcome variables that capture those base objectives. 2. Select a causally representative subset of the outcome variables to serve as reward terms. 3. Fit weights for these reward terms through preference-guided feedback.

This paper's contributions describe Step 1 as a guided workflow and formalize Steps 2 and 3:

Step 1: A guided workflow for deriving outcome variables.
Step 2: Reward-term selection is reduced to a minimum-cost partial cover problem on a causal DAG, solved in polynomial time via max-flow.
Step 3: Weight fitting is framed as a convex feasibility problem, iteratively shrunk via preference queries and solved by an existing separating-oracle method.

To the authors' knowledge, this is the first reward-design method that preserves a deterministic, conflict-free feasible weight region, shrinking it to a desired tolerance in O(n log κ) preference queries through a separating oracle.

Key Points

Goal: Make reward-function design accessible to non-experts while producing human-aligned (preference-consistent) reward functions.
Step 1 – Outcome Derivation: A guided workflow that translates natural-language task descriptions into measurable outcome variables tied to base objectives.
Step 2 – Causal Reward-Term Selection: Formulated as a minimum-cost partial cover over a causal DAG; solvable in polynomial time using max-flow algorithms.
Step 3 – Preference-Based Weight Fitting: Modeled as a convex feasibility problem; uses a separating-oracle approach over preference queries.
Convergence Guarantee: Iteratively shrinks the feasible weight region to a target tolerance in O(n log κ) preference queries, maintaining a deterministic, conflict-free feasible set throughout the process.
Significance: First reward-design framework to formally guarantee preservation of a non-conflicting feasible weight region while iterating under preference constraints.

Source

Original (Chinese) summary auto-collected from zhichai.net on 2026-08-14.
Paper link: https://arxiv.org/abs/2508.03415

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