# Good Rankers, Bad Objectives: Bilinear Contrastive Critics under Expressive Policy Search

arXiv: https://arxiv.org/abs/2607.27422 · HTML: https://mlsanity.com/paper/2607.27422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 16 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Contrastive Learning as Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2206.07568/) (2022)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Cal-QL: Calibrated Offline RL Pre-Training for Efficient Online Fine-Tuning](https://mlsanity.com/paper/2303.05479/) (2023)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making](https://mlsanity.com/paper/2406.17098/) (2024)
- [Diffusion-DICE: In-Sample Diffusion Guidance for Offline Reinforcement Learning](https://mlsanity.com/paper/2407.20109/) (2024)
- [EXPO: Stable Reinforcement Learning with Expressive Policies](https://mlsanity.com/paper/2507.07986/) (2025)
- [Stabilizing Contrastive RL: Techniques for Robotic Goal Reaching from Offline Data](https://mlsanity.com/paper/2306.03346/) (2023)
- [RankQ: Offline-to-Online Reinforcement Learning via Self-Supervised Action Ranking](https://mlsanity.com/paper/2605.11151/) (2026)

## Abstract (arXiv)

Good action rankings do not make a contrastive critic safe to maximize. These critics increasingly act as value-like objectives for best-of-K selection, planning, and critic-guided generation. Unbounded bilinear scores can let large embedding norms inflate off-support values, but cosine bounding does not remove the failure. A controlled support decomposition attributes most raw bilinear regret to norm drift. Cosine and hybrid critics nevertheless select off-support actions from most pools and incur comparable regret. Contrastive scores are weakly calibrated or inverted in the top score decile across four OGBench navigation tasks, and they fail to order fixed-query actions by value. Bellman-trained TD-Q succeeds, including in a parameter-matched function-class control. Realized costs depend on the task: simulator rollouts reveal single-step selection costs on PointMaze and the exact-Q^* toy but well-powered nulls on AntMaze and HumanoidMaze, where the controller can self-correct. A training/readout decomposition traces the lost ordering to the cosine training objective; raw-trained embeddings retain weak ordering after inference-time normalization. Candidate maximization can therefore exploit false positives caused by norm drift, score saturation, or in-support misranking. Contrastive critics remain useful compatibility rankers on navigation and manipulation tasks, but action selection requires a value-calibrated scalar.