Support sufficiency as action-sufficient compression: a single-cycle rate-regret formulation

A theoretical computer science paper formalizes decision-making under information constraints as action-sufficient compression, where systems need only preserve distinctions relevant to choosing optimal actions rather than reconstructing full state information. The framework applies rate-distortion theory to support states with regret-based distortion, offering a mathematical foundation for robust single-cycle arbitration.

This paper addresses a fundamental challenge in decision theory: how much information a decision-maker must retain to act optimally. Rather than requiring complete reconstruction of underlying states, the authors prove that systems only need to preserve distinctions that affect action selection under given consequence structures. This distinction separates action adequacy from reconstruction fidelity—a critical insight for efficient decision-making architectures.

The theoretical contribution builds on information theory and rate-distortion principles, traditionally applied to compression and communication. By reframing support sufficiency as action-sufficient compression with regret-based distortion, the work provides a unifying mathematical language for when and why simpler decision policies suffice. The policy equivalence approach elegantly explains failure modes of existing methods that either ignore confidence signals entirely or treat them as scalar quantities, showing these approaches fail precisely when they partition information across action boundaries.

For machine learning and AI systems, this formalization carries practical implications. It provides theoretical justification for attention mechanisms, information bottlenecks, and model compression strategies that prioritize decision-relevant features. The bounded expected policy regret framework offers measurable criteria for when information pruning remains acceptable versus when additional context becomes necessary.

The work distinguishes itself from rational inattention and information-bottleneck literature by focusing explicitly on action consequence geometry rather than prediction accuracy. This orientation makes it directly applicable to robotics, autonomous systems, and trading algorithms where action selection is the primary objective. Future research may extend single-cycle results to multi-stage decision problems and incorporate dynamic consequence structures.

• →Action-sufficient compression requires preserving only distinctions relevant to optimal action selection, not full state reconstruction
• →Policy equivalence creates exact partitions where states can merge when they require identical optimal actions
• →The framework applies rate-distortion theory with regret-based distortion rather than traditional reconstruction error
• →Existing content-only and scalar-confidence approaches fail specifically when induced partitions cross action boundaries
• →Consequence geometry determines information relevance, making decision context fundamental to compression requirements