# The Informational Cost of Agency: A Bounded Measure of Interaction Efficiency for Deployed Reinforcement Learning

arXiv: https://arxiv.org/abs/2603.01283 · HTML: https://mlsanity.com/paper/2603.01283/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Legged Locomotion in Challenging Terrains using Egocentric Vision](https://mlsanity.com/paper/2211.07638/) (2022)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Empowerment -- an Introduction](https://mlsanity.com/paper/1310.1863/) (2013)
- [Unsupervised Concept Drift Detection from Deep Learning Representations in Real-time](https://mlsanity.com/paper/2406.17813/) (2024)
- [Mutual Information Tracks Policy Coherence in Reinforcement Learning](https://mlsanity.com/paper/2509.10423/) (2025)
- [Entropy-Based Non-Invasive Reliability Monitoring of Convolutional Neural Networks](https://mlsanity.com/paper/2508.21715/) (2025)
- [A Mathematical Theory of Agency and Intelligence](https://mlsanity.com/paper/2602.22519/) (2026)

## Abstract (arXiv)

Deployed reinforcement learning systems lack a principled runtime reliability theory. We close this gap by introducing Bipredictability, P, a closed form information theoretic metric that quantifies how efficiently a closed loop interaction between agent and environment converts uncertainty into shared predictability. P admits a provable classical bound P equal, smaller than 0.5, derived from Shannon entropy subadditivity, and responsive agency necessarily suppresses P below this ceiling, a structural prediction we term the informational cost of agency. Across 21 trained continuous control agents, we confirm this prediction empirically at P = 0.33 plus minus 0.02. The same suppression signature reproduces in language model dialogue, convolutional vision systems, and classical mechanical baselines, indicating that P captures a substrate independent property of agentic interaction rather than an algorithm specific artifact. The Information Digital Twin, IDT, a model agnostic architecture that computes P from the external interaction stream, detects 89.3% of coupling degradations against 44.0% for reward based monitoring, with 4.4 times lower latency. P provides the missing measurement layer for runtime reliability and closed loop self regulation in deployed autonomous systems.