Adaptive Sensing beyond Non-Adaptive Information Limits: End-to-End Co-Design of Geometry, Policy, and Inference

TL;DR

This paper introduces a joint dynamic programming approach for co-designing sensor geometry and adaptive measurement policies, significantly improving information capture and reducing errors across various sensing applications.

Contribution

It formulates a differentiable, bias-free joint optimization framework for hardware and policy co-design, extending from small POMDPs to large-scale photonic topologies.

Findings

Joint-DP outperforms traditional geometry selection in radar POMDPs by 2.8x.

Reduces mean-squared error by 11.3x in superconducting-qubit flux sensors.

Achieves 123x reduction in error over randomized baselines in photonic metasensors.

Abstract

Inverse design has made vast physical parameter spaces a substrate for emergent behavior. In sensing, the stakes of this principle are sharpest at the analog-to-digital boundary, where any information the hardware fails to capture is information no downstream algorithm can recover; hardware optimization alone is therefore not enough, and the geometry must be co-designed with a rule for what to measure next. We formulate this co-design as \emph{joint dynamic programming} (joint-DP): a single optimization over the continuous hardware geometry and a Bellman-optimal adaptive measurement policy. The outer hardware gradient is computed by differentiable dynamic programming with a sharp Bellman maximum, which the envelope theorem makes exact and bias-free, and a relaxation hierarchy carries the common framework from small discrete POMDPs to $10^5$-pixel photonic topologies. Across three case studies, joint-DP beats the natural baseline of its community by a large factor: on a radar beam-search POMDP, classical information-bound-guided geometry selection loses $2.8\times$ in attainable adaptive value; on a superconducting-qubit flux sensor, joint-DP reduces deployed mean-squared error by $11.3\times$ over the joint Bayesian Cram\'er--Rao baseline, with both geometries numerically co-optimized under their respective objectives; and on a $90{,}000$-pixel photonic metasensor, joint-DP via the Bayesian Fisher-information-matrix surrogate reduces deployed mean-squared error by $123\times$ relative to a randomized baseline. For any sensor whose hardware is designed once but whose policy runs for the device's lifetime, joint optimization of hardware and policy is the minimum principled procedure.