Value of Information

Partially observable Markov decision processes (POMDPs) offer a principled formalism for planning under state and transition uncertainty. Despite advances made towards solving large POMDPs, obtaining performant policies under limited planning time remains a major challenge due to the curse of dimensionality and the curse of history. For many POMDP problems, the value of information (VOI) - the expected performance gain from reasoning about observations - varies over the belief space. We introduce a dynamic programming framework that exploits this structure by conditionally processing observations based on the value of information at each belief. Building on this framework, we propose Value of Information Monte Carlo planning (VOIMCP), a Monte Carlo Tree Search algorithm that allocates computational effort more efficiently by selectively disregarding observation information when the VOI is low, avoiding unnecessary branching of observations. We provide theoretical guarantees on the near-optimality of our VOI reasoning framework and derive non-asymptotic convergence bounds for VOIMCP. Simulation evaluations demonstrate that VOIMCP outperforms baselines on several POMDP benchmarks.

Autonomous tool-using agents in networked environments must decide which information source to query and when to stop querying and act. Without principled bounds on information-acquisition costs, unconstrained agents exhibit systematic failure modes: excessive tool use under congestion, prolonged deliberation under time decay, and brittle behavior under ambiguous evidence. We propose the Triadic Cognitive Architecture (TCA), a decision-theoretic framework that formalizes these failure modes via cognitive friction. By combining nonlinear filtering, congestion-dependent cost dynamics, and HJB optimal stopping, TCA models deliberation as stochastic control over a joint belief-congestion state, explicitly pricing information by tool signal quality and live network load. TCA yields an HJB-inspired stopping boundary and a computable rollout-based approximation of belief-dependent value-of-information with a net-utility halting condition. We validate TCA in two controlled environments (EMDG and NSTG) designed to isolate stopping quality, action selection under congestion, and temporal urgency. TCA improves resource outcomes while reducing time-to-action without degrading accuracy, gaining 36 viability points in EMDG and 33 integrity points in NSTG over greedy baselines. Ablations show that selection and stopping must be optimized jointly, as stopping rules alone recover at most 4 viability points. Sensitivity sweeps over alpha, beta, and lambda_S yield stable accuracy and interpretable trade-offs, and a continuation-value sweep over eta values 0, 0.1, 0.3, and 0.5 finds eta equal to zero is optimal under high temporal urgency. Finally, we demonstrate an illustrative instantiation around a black-box LLM on a memorisation-free corpus, where the same stopping principle executes using empirically computable uncertainty and value-of-information proxies.

Current Retrieval-Augmented Generation (RAG) systems predominantly rely on relevance-based dense retrieval, sequentially fetching documents to maximize semantic similarity with the query. However, in knowledge-intensive and real-world scenarios characterized by conflicting evidence or fundamental query ambiguity, relevance alone is insufficient for resolving epistemic uncertainty. We introduce Entropic Claim Resolution (ECR), a novel inference-time algorithm that reframes RAG reasoning as entropy minimization over competing semantic answer hypotheses. Unlike action-driven agentic frameworks (e.g., ReAct) or fixed-pipeline RAG architectures, ECR sequentially selects atomic evidence claims by maximizing Expected Entropy Reduction (EER), a decision-theoretic criterion for the value of information. The process dynamically terminates when the system reaches a mathematically defined state of epistemic sufficiency (H <= epsilon, subject to epistemic coherence). We integrate ECR into a production-grade multi-strategy retrieval pipeline (CSGR++) and analyze its theoretical properties. Our framework provides a rigorous foundation for uncertainty-aware evidence selection, shifting the paradigm from retrieving what is most relevant to retrieving what is most discriminative.

Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the agents' cost structures. When cost parameters are uncertain, the recommended actions may no longer be incentive compatible, allowing agents to benefit from deviating from them. We study a chance-constrained correlated equilibrium problem formulation that accounts for uncertainty in agents' costs and guarantees incentive compatibility with a prescribed confidence level. We derive sensitivity results that quantify how uncertainty in individual incentive constraints affects the expected coordination outcome. In particular, the analysis characterizes the value of information by relating the marginal benefit of reducing uncertainty to the dual sensitivities of the incentive constraints, providing guidance on which sources of uncertainty should be prioritized for information acquisition. The results further reveal that increasing the confidence level is not always beneficial and can introduce a tradeoff between robustness and system efficiency. Numerical experiments demonstrate this tradeoff: CC-CE reduces realized coordination cost by up to 35% at intermediate confidence levels, while the proposed information-gain metric consistently identifies effective uncertainty sources to reduce.

Large language models are beginning to show steganographic capabilities. Such capabilities could allow misaligned models to evade oversight mechanisms. Yet principled methods to detect and quantify such behaviours are lacking. Classical definitions of steganography, and detection methods based on them, require a known reference distribution of non-steganographic signals. For the case of steganographic reasoning in LLMs, knowing such a reference distribution is not feasible; this renders these approaches inapplicable. We propose an alternative, decision-theoretic view of steganography. Our central insight is that steganography creates an asymmetry in usable information between agents who can and cannot decode the hidden content (present within a steganographic signal), and this otherwise latent asymmetry can be inferred from the agents' observable actions. To formalise this perspective, we introduce generalised $\mathcal{V}$-information: a utilitarian framework for measuring the amount of usable information within some input. We use this to define the steganographic gap -- a measure that quantifies steganography by comparing the downstream utility of the steganographic signal to agents that can and cannot decode the hidden content. We empirically validate our formalism, and show that it can be used to detect, quantify, and mitigate steganographic reasoning in LLMs.

Bayesian optimal experimental design provides a principled framework for selecting experimental configurations that maximize obtained information. In this work, we consider settings where the likelihood entropy is independent of the design or can be evaluated explicitly, which applies, e.g. to additive noise models with design-independent or explicitly computable noise entropy. This reduces the problem to maximum entropy estimation, where the nested integral defining the expected information gain collapses into a single integral. Our study is motivated by large-scale inference problems, such as inverse problems, where the computational cost is dominated by expensive likelihood evaluations. Under additive Gaussian noise model, we propose a computational approach in which the evidence density is approximated by a Monte Carlo or quasi-Monte Carlo surrogate, while the differential entropy is evaluated using standard methods without additional likelihood evaluations. We prove that this strategy achieves convergence rates that are comparable to, or better than, state-of-the-art methods for full expected information gain estimation, particularly when the cost of entropy evaluation is negligible. Our approach relies only on mild smoothness of the forward map and avoids stronger technical assumptions required in earlier work. We also present numerical experiments, which confirm some of our theoretical findings.

Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the policy under such constraints. Here, we in- stead suggest that fairness can be directly analyzed as a property of the utility function. Instead of imposing fairness constraints on the policy, we suggest to simply maximize a utility function satisfying certain fairness properties. Concretely, we define value of information fairness, which prescribes that there must not be an incentive to infer the protected attribute. This principle sug- gests modifying utility functions such that they satisfy value of information fairness. We describe how such modifications can be achieved and discuss consequences for the corresponding optimal policies. We apply our framework to thought experiments and the COMPAS data, demonstrating that focusing on utility functions sometimes provides answers that better align with intuitive judg- ments about what is fair. Moreover, we are not aware of any intuitively fair policy that violates value of information fairness; and when we find that value of information fairness recommends an intuitively unfair policy, no realizable policy is intuitively fair.