information gain analysis

This work investigates the quantitative trade-off between accumulated information (in bits) and cumulative regret (i.e., reward loss) in sequential decision-making. Under the Bayesian setting, we establish the first information-dependent lower bound on regret. Methodologically, we unify information theory, Bayesian optimal decision analysis, and regret decomposition to construct a coherent theoretical framework wherein information and regret are exchangeable—systematically integrating and generalizing several classical regret lower bounds. We empirically validate the tightness of our bounds via question-answering tasks using large language models (LLMs). Experimental results demonstrate that incorporating information-aware policies significantly reduces regret in LLM-based QA, providing empirical evidence for the validity and practical utility of a quantifiable information–regret trade-off.

This paper investigates the information evolution mechanism in interactive decision-making for stochastic multi-armed bandits. To characterize the dynamic relationship between the optimal success probability and mutual information over time, we propose a time-resolved joint analytical framework integrating information-theoretic measures (mutual information, KL divergence) with asymptotic statistical analysis. We establish, for the first time, a three-phase growth pattern of mutual information—linear → quadratic → linear—and rigorously prove that this non-monotonic evolution arises intrinsically from interaction, contrasting sharply with non-interactive settings. Furthermore, we demonstrate that optimal learning and maximal information gain are decoupled, challenging the conventional “information maximization implies optimal learning” assumption. Our results provide the first precise temporal information benchmark and theoretical foundation for interactive learning. (132 words)

This work addresses the challenge of suboptimal human decision-making under uncertainty, where individuals often struggle to determine when to stop information search due to high cognitive load. While existing AI assistance primarily focuses on optimizing final outcomes, it frequently neglects low-burden support during the search process itself. To bridge this gap, the authors propose SERA, a conversational decision-support system powered by large language models that introduces feedback granularity—summary versus verbatim—as a core design variable. SERA generates real-time, cognitively grounded information-gain feedback across three uncertainty scenarios. Experimental results demonstrate that SERA significantly improves both decision accuracy and confidence: summary feedback curbs over-sampling, while verbatim feedback encourages deeper exploration, with pronounced benefits under high uncertainty. This approach establishes a novel paradigm for adaptive, process-oriented decision support.

In information provision experiments, standard two-stage least squares (TSLS) and panel estimators systematically underestimate the average partial effect (APE) because their weighting schemes assign higher weights to individuals with stronger first-stage belief updates—thereby over-downweighting weak updaters. This weighting bias arises from the implicit assumption of unweighted identification in conventional instrumental variable (IV) methods, which fails under heterogeneous belief updating. We propose a Bayesian belief-updating–based control function approach that achieves unbiased, unweighted APE identification without relying on update strength. By decoupling estimation from update intensity, our method corrects TSLS’s upward bias toward strong updaters. Applied to a gender wage gap beliefs experiment, our estimator yields an APE 40% larger than TSLS, substantially improving causal inference accuracy. Our key contribution is the first structural identification framework enabling consistent estimation of the unweighted APE.

This paper identifies that algorithmic recommendations not only update decision-makers’ beliefs but also reshape their preferences by establishing themselves as default anchors—inducing “recommendation-dependent preferences” that lead to excessive compliance and Pareto inefficiency. To address this, we formally model this preference-shaping mechanism and develop a behavioral game-theoretic framework integrating Bayesian belief updating and counterfactual evaluation, proving that standard recommendation mechanisms reduce social welfare under preference dependence. We then propose a preference-aware recommendation calibration framework, wherein recommendation intensity is endogenously regulated via mechanism design. Experiments in judicial and medical simulation settings demonstrate that our calibration algorithm significantly reduces excessive compliance while improving decision efficiency and social welfare. Our core contributions are: (i) the first formal identification and modeling of algorithms’ preference-shaping effect, and (ii) the first falsifiable, implementable calibration scheme for mitigating such effects.

This study addresses how agents balance immediate action against seeking clarifying information under uncertainty. The authors propose a computational model based on expected regret that formally characterizes, for the first time, how contextual uncertainty and action costs jointly influence human decisions to ask clarification questions. Using an experimental paradigm that integrates both linguistic clarification and non-linguistic action choices, the research demonstrates that individuals’ propensity to seek clarification increases with the potential loss associated with erroneous actions, thereby validating the proposed rational trade-off mechanism. These findings reveal a cognitive strategy wherein humans proactively reduce uncertainty in high-stakes situations to avoid significant losses, offering both theoretical and empirical support for understanding metacognitive decision-making in communicative contexts.

This paper investigates the sample complexity of function estimation and optimization in Gaussian process regression, focusing on the intrinsic relationship between information gain and effective dimensionality—and its sensitivity to observation noise. To address this, we introduce *relative information gain*, a novel metric that quantifies the robustness of information gain under noise perturbations and reveals its smooth interpolation behavior between information gain and effective dimensionality. This metric is naturally embedded in PAC-Bayesian excess risk bounds, enabling theoretical unification. Leveraging tools from reproducing kernel Hilbert space theory, spectral analysis, and information theory, we derive upper bounds on relative information gain that explicitly depend on the kernel’s spectral decay rate. Based on these bounds, we establish minimax-optimal convergence rates, substantially improving both the precision and generality of sample complexity analysis in nonparametric Bayesian learning.

This study addresses the problem of identifying which agent—either a decision-maker or an advisor—possesses more information in settings where only observed actions and outcomes are available. Focusing on multi-armed bandit environments, the work proposes the first scoring test framework capable of distinguishing the better-informed agent without requiring counterfactual information. By integrating game-theoretic modeling with theoretical analysis, the paper characterizes the identifiability boundaries under both simultaneous and sequential decision-making protocols. The key contributions reveal that, in the simultaneous setting, an effective scoring test exists; however, in the sequential setting, no scoring test can simultaneously guarantee accurate identification and achieve social welfare exceeding 50% of the optimum, thereby exposing a fundamental trade-off between information identification and welfare maximization.

This study addresses the multi-armed bandit problem augmented with an oracle that can reveal the optimal action at a cost, investigating whether such query capability reduces regret under standard bandit feedback where only the reward of the chosen action is observed. By integrating information-theoretic lower bounds, stochastic process analysis, and adaptive algorithm design, the work provides the first complete characterization of the value of this querying mechanism and uncovers fundamental differences between adversarial or correlated environments and i.i.d. settings. The main contributions include establishing a regret lower bound of Ω(√(T−k)) in adversarial or correlated environments, and achieving matching upper and lower bounds of Õ(min{T/k, √(T−k)}) in the i.i.d. case, thereby rigorously quantifying how the number of queries k fundamentally governs learning performance.

Traditional machine learning relies on explicit parametric models and strong distributional assumptions, limiting flexibility, interpretability, and adaptability to dynamic data updates. To address these limitations, this paper proposes a model-free information-theoretic framework—*information mechanics*—that directly quantifies uncertainty in raw data via surprisal, bypassing explicit probabilistic modeling. The approach is parameter-free, traceable, and editable (supporting incremental data addition/deletion), enabling universal inference. Its core conceptual contribution redefines learning as uncertainty measurement and establishes fundamental “physical laws” at the information level, unifying diverse tasks including generative inference, causal discovery, anomaly detection, and time-series forecasting. Experiments demonstrate performance at or near state-of-the-art across multiple benchmarks; the method natively handles missing data and preserves full human interpretability throughout the inference process.