networked control engineers

Abstract: In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate $Q$-functions, but a naive order-$n$ expansion over $N$ agents requires $Θ(N^n)$ coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.

Abstract: We study decentralized optimization with cross-coupled mixed affine constraints, where local and shared variables interact through two affine channels. We show that the intrinsic difficulty of combining separately well-conditioned channels is governed by their Friedrichs angle. This geometry induces a cross-coupling factor that cannot be removed by channelwise preconditioning and governs the additional affine-oracle and communication complexity. We develop an accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime and extend the framework to smooth and nonsmooth convex objectives. Experiments confirm the predicted dependence on cross-channel geometry and network conditioning.

Abstract: We propose a pragmatic information theory unifying communication, control, and decision-making. Its core is the isoteleia mapping, formalizing equifinality: distinct semantic paths leading to the same optimal action are pragmatically equivalent. This induces a three-tier hierarchy of syntactic, semantic, and pragmatic information, each abstraction discarding task-irrelevant distinctions. We develop pragmatic entropy, up/down mutual information, channel capacity, and rate-distortion, and prove three coding theorems generalizing Shannon's classical results. We introduce pragmatic value (VoI) and cost (CoI) of information as decision-theoretic duals to rate-distortion and capacity, respectively, and formulate a Lagrangian dual framework for cross-layer optimization. The pragmatic efficiency bound $\mathcal{E}_p(λ)=\sup_R[Φ_p(R)-λ\,\mathrm{CoI}_p(R)]$ quantifies the maximum net utility any resource-constrained intelligent system can extract, thereby establishing a fundamental behavioral capacity limit---generalizing Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages yield closed-form Gaussian expressions, while dynamic settings are addressed via a Bellman equation for sequential decision-making. This framework provides a rigorous foundation for task-oriented communication, networked control, autonomous systems, and embodied AI, shifting focus from symbol fidelity to the effectiveness of information in guiding actions, and offers a unified mathematical language for next-generation intelligent systems.