Reward Learning through Ranking Mean Squared Error

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, long

Summary

Chaitanya Kharyal, Calarina Muslimani, and Matthew E. Taylor introduce Ranked Return Regression for RL (R4), a novel rating-based reinforcement learning method designed to overcome the reward design bottleneck in real-world RL applications. R4 infers reward functions from human feedback provided as discrete, multi-class ratings (e.g., "bad," "neutral," "good") for agent trajectories. The core of R4 is a new ranking mean squared error (rMSE) loss, which treats these ratings as ordinal targets. This approach uses a differentiable sorting operator (soft ranks) to optimize the mean squared error between predicted returns' soft ranks and teacher ratings. Unlike prior rating-based methods, R4 offers formal guarantees of minimality and completeness under mild assumptions. Empirically, R4 consistently matches or outperforms existing rating and preference-based RL algorithms on robotic locomotion benchmarks from OpenAI Gym and the DeepMind Control Suite, while requiring significantly less feedback.

Key takeaway

For Machine Learning Engineers designing rewards for complex RL tasks, R4 offers a robust solution. If you are currently using preference-based methods, consider switching to rating-based feedback with R4 to significantly reduce the required human effort. This approach provides provable guarantees and empirically outperforms existing methods on robotic locomotion, enabling more efficient and reliable reward function inference for your agents.

Key insights

R4 uses a novel ranking MSE loss to learn RL rewards from ordinal human ratings, outperforming prior methods with less feedback.

Principles

• Reward functions can be inferred from human feedback.
• Multi-class ratings offer richer feedback than binary preferences.
• Differentiable sorting enables gradient propagation through ranking.

Method

R4 samples trajectory-rating pairs, predicts returns, ranks them using a differentiable soft sorting operator, then optimizes a mean squared error loss between soft ranks and teacher ratings.

In practice

• Apply R4 for efficient reward learning in robotics.
• Use multi-class ratings for richer human feedback.
• Leverage rMSE loss for provably minimal reward functions.

Topics

• Reward Learning
• Rating-based RL
• Ranking Mean Squared Error
• Robotic Locomotion
• Human Feedback
• OpenAI Gym

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Robotics Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.