Information Gain

Information-theoretic exploration is of primary interest in methodological studies of reinforcement learning (RL) and computational cognitive neuroscience, while the established RL theory builds regret guarantees on confidence sets. This situation leaves open the conditions under which the information-driven exploration found in nature is more advantageous than the exploration of the established RL theory. We put the state-of-the-art methods of these two paradigms, Active Inference (AIF) and Bayes-UCBVI, on an equal footing: both act through the same state abstraction of a tabular MDP with $S$ states, and their greedy forms differ only in the exploration term. We find that AIF's information gain decays too fast to serve as a confidence width, locking greedy agents that explore by it out of the optimal action. Calibrating the information gain by a square root yields calibrated AIF, which attains regret of order $\sqrt T$ for an exact abstraction, but no better guarantee than Bayes-UCBVI for a fixed reward. When an adversary chooses rewards from the agent's data, Bayes-UCBVI's value-specific widths lock out, whereas calibrated AIF pays a factor $\sqrt S$, which no goal-memoryless agent avoids on some MDP whose start states the adversary also chooses. Calibrated information gain thus acts as a reward-agnostic $\ell_1$ confidence set, preferable to value-specific widths when rewards are chosen from the agent's data, not when they are fixed.

Radiance fields need hundreds of views, and their placement matters as much as their number. Next-best-view (NBV) selection for 3D Gaussian Splatting (3DGS) usually scores every candidate in the pool and keeps one. Searching for information and choosing a camera, however, are separable problems. We present AGILE-GS, an anchor-guided NBV method that separates the two. A virtual anchor pose is optimized on SE(3) by Riemannian gradient ascent on expected information gain. It need not be reachable or in the pool; it marks where the model is most uncertain. Candidates are scored against the anchor's viewing geometry, and a greedy ridge-leverage step distills the pool into a small, non-redundant shortlist without rendering any candidate. The shortlist can be used in two ways. AGILE-GS takes the first view on it as the next view, so no Fisher information is computed for any candidate. AGILE-GS+ computes the Fisher information gain of each shortlisted view and picks the best, so the expensive evaluation runs on a handful of views rather than the whole pool. On standard benchmarks and in closed-loop embodied acquisition, both match or exceed existing baselines while cutting selection latency by one to two orders of magnitude.

"System One" decision models such as TypeSafe's Jev and its open counterpart Laya answer typed questions about a text in a single forward pass with calibrated probabilities, but they cannot ask for missing information: when a first message does not say what separates two departments, they guess. We present LAVOIR (Laya with Value-Of-Information Routing), which places the candidate pieces of missing information (slots) in the input next to the answer options, so that one forward pass returns both the decision distribution and, for every slot, the expected gain in the probability of the correct decision if the user were asked about it. VOI targets need no human labels: gold decisions come from schema rules, an LLM only verbalizes messages and answers, a model from another family checks every text, and pairing each message with several profiles makes regression on realized gains estimate the expected gain. A Gini-impurity cap bounds the predicted value by what a calibrated model can still gain. In a controlled study, decisions on seen schemas are statistically indistinguishable from the Bayes ceiling. The final model's question policy matches a greedy oracle VOI policy on seen schemas (AUC 0.799 vs. 0.797), and with at most 0.5 questions per conversation it is 14.1 points more accurate than never asking. On real ABCD conversations, one real exchange raises accuracy by 8.3 points where LAVOIR asks and leaves it unchanged where it does not; on SGD the cap lowers the asking rate from 93% to 8.6%. On Laya's twelve benchmarks LAVOIR is above Laya's reported scores on seven, and it answers a question in 31 ms (median, GH200).

Recent advances in large language models (LLMs) have enabled their use as conversational recommender systems (CRS), demonstrating strong recommendation accuracy and natural dialogue. However, guiding multi-turn interactions to elicit user preferences effectively remains challenging. Existing approaches either use separate reinforcement learning agents with templated interactions or optimize for interactivity judged by another LLM, without measuring how much useful information is actually gained. We propose a new approach that quantifies the effectiveness of each interaction by the reduction in the assistant's uncertainty, measured via entropy over recommendations. We apply this entropy reduction as a reward---without relying on ground-truth recommendations, which are often unavailable in real-world scenarios---to fine-tune the LLM, enabling strategic interaction generation. Empirical results with supervised fine-tuning (SFT) and direct preference optimization (DPO) on the INSPIRED and ReDial datasets show that our method improves both recommendation quality and conversational efficiency.

Active 3D reconstruction relies on active view selection to maximize reconstruction fidelity under limited capture budgets. However, most existing methods rely on surrogate signals such as parameter uncertainty or geometric heuristics, but these signals are often misaligned with the ultimate goal: the fidelity of rendered predictions. We propose GO-PRE, a goal-oriented next-best-view selection framework that explicitly targets information gain in the prediction space. Specifically, we formulate the objective as maximizing the reduction of the average marginal predictive entropy over a user-specified target view manifold. GO-PRE supports interactive goal specification and yields an efficient acquisition rule that enables real-time computation of information gain. Extensive experiments across benchmarks demonstrate that GO-PRE consistently improves active reconstruction performance and provides more reliable uncertainty quantification compared to state-of-the-art methods.

This paper presents an information-gain-guided reinforcement-learning sensor-selection framework for single-vessel tracking in heterogeneous maritime sensor networks. The proposed approach is motivated by information-theoretic sensor management: instead of activating all sensors or repeatedly performing computationally expensive online expected-information-gain evaluation, a learned policy selects one tracking-relevant sensor at each decision epoch. A Bayesian sequential Monte Carlo tracker estimates the vessel state from noisy measurements and provides a belief representation for scheduling under nonlinear and non-Gaussian conditions. A Proximal Policy Optimization agent selects one of five sensors in a georeferenced simulation of the CMMI Smart Marina testbed at Ayia Napa Marina, Cyprus. The policy is trained on the testbed's actual five-sensor configuration. The agent observes belief-state, detection-history, coverage, sensor-geometry, and realized-information-gain features. The reward is defined as a realized-information-gain term gated by an observability mask. Final-test simulations compare the proposed framework with random single-sensor selection, always-on sensing using all sensors simultaneously, and the expected-information-gain sensor-selection baseline proposed in our previous work. Results show that the learned policy achieves tracking performance close to always-on sensing while activating only one sensor per decision time step and avoiding the computationally expensive online entropy search required by expected-information-gain selection. Additional zero-shot evaluation without retraining on ten moderately perturbed versions of actual layout configuration showed broadly stable tracking, with any increase in positional tracking error remaining below 1 meter across all perturbations.

Instance Goal Navigation (IGN) requires an embodied agent to find a specific object instance among distractors from an under-specified natural-language description. Such ambiguity often cannot be resolved from perception and language alone, making interaction with an oracle a natural mechanism for disambiguation. Prior interactive methods allow oracle queries but treat lightweight clarification and route-level guidance alike, letting agents boost success rate through repeated high-information questions rather than by resolving the underlying ambiguity efficiently. We recast interactive IGN as a cost-sensitive uncertainty-reduction problem, where the agent should ask the question whose answer provides the largest reduction in navigation uncertainty relative to its penalty. To this end, we apply an information-gain analysis on existing navigation corpora to identify which cues reduce navigation uncertainty, yielding a compact set of question types and data-derived weights. However, existing interactive navigation benchmarks do not model the cost of different question types or evaluate how efficiently agents use interaction, making them unsuitable for studying cost-sensitive interaction. Based on this taxonomy, we construct a benchmark for diagnosing interaction behavior and efficiency, together with a Weighted Success Rate metric that penalizes each query by its derived cost. We further propose a zero-shot MLLM navigator that selectively queries at each decision step only when the expected uncertainty reduction justifies the interaction cost.

Large Language Model (LLM) agents often operate under underspecified user instructions, where latent uncertainty over user intent leads to erroneous tool actions. To address this challenge, we propose a goal-oriented clarification framework that aligns clarification behavior with ambiguity resolution. Central to our approach is the Information Gain Reward, a metric that quantifies the utility of clarification questions by measuring the Bayesian belief update towards the ground-truth goal induced by the clarification exchange. We train the clarifier (LLM) using this reward to optimize for high information gain, ensuring that clarifications effectively reduce uncertainty and improve task completion within the agent-tool-user environment. We validate our framework within a clarification-enhanced $τ$-Bench environment, conducting cross-agent evaluations across five heterogeneous backbones. Empirical results demonstrate that our method consistently improves the success rate by 3.7% over the no-clarification baseline, while adding only 0.3 total interaction steps on average.

Intrinsic rewards for exploration in reinforcement learning condition on different contexts: lifelong rewards score each transition against accumulated experience but ignore within-rollout redundancy; episodic rewards penalize intra-trajectory repetition but discard lifetime progress. Hybrid methods combine both signals through heuristic weights or require Gaussian-process dynamics that do not scale beyond low-dimensional state spaces. Trajectory-level information gain decomposes into per-step terms that condition on the replay buffer and rollout prefix simultaneously, but remains intractable for deep models. We derive the Conditional Information Gain (CIG) reward as a tractable surrogate: a log-determinant objective over an ensemble disagreement kernel whose Cholesky factorization yields causal per-step rewards that retain both conditioning sets while scaling to high-dimensional state spaces. We instantiate CIG in a model-based setting, where rollouts are short and within-rollout corrections remain largely unexplored. Across twelve tasks spanning discrete (MiniGrid) and continuous control (OGBench), in both clean and stochastic-distractor settings, CIG outperforms or matches prior exploration methods while remaining robust to stochastic distractors.

Robotic exploration in large-scale environments is computationally demanding due to the high overhead of processing extensive frontiers. This article presents an OctoMap-based frontier exploration algorithm with predictable, asymptotically bounded performance. Unlike conventional methods whose complexity scales with environment size, our approach maintains a complexity of $\mathcal{O}(|\mathcal{F}|)$, where $|\mathcal{F}|$ is the number of frontiers. This is achieved through strategic forward and inverse sensor modeling, which enables approximate yet efficient frontier detection and maintenance. To further enhance performance, we integrate a Bayesian regressor to estimate information gain, circumventing the need to explicitly count unknown voxels when prioritizing viewpoints. Simulations show the proposed method is more computationally efficient than the existing OctoMap-based methods and achieves computational efficiency comparable to baselines that are independent of OctoMap. Specifically, the Bayesian-enhanced framework achieves up to a $54\%$ improvement in total exploration time compared to standard deterministic frontier-based baselines across varying spatial scales, while guaranteeing task completion. Real-world experiments confirm the computational bounds as well as the effectiveness of the proposed enhancement.

Generative virtual staining (VS) models for high-throughput screening (HTS) can provide an estimated posterior distribution of possible biological feature values for each input and cell. However, when evaluating a VS model, the true posterior is unavailable. Existing evaluation protocols only check the accuracy of the marginal distribution over the dataset rather than the predicted posteriors. We introduce information gain (IG) as a cell-wise evaluation framework that enables direct assessment of predicted posteriors. IG is a strictly proper scoring rule and comes with a sound theoretical motivation allowing for interpretability, and for comparing results across models and features. We evaluate diffusion- and GAN-based models on an extensive HTS dataset using IG and other metrics and show that IG can reveal substantial performance differences other metrics cannot.

Large language models (LLMs) are increasingly used for diagnostic tasks in medicine. In clinical practice, the correct diagnosis can rarely be immediately inferred from the initial patient presentation alone. Rather, reaching a diagnosis often involves systematic history taking, during which clinicians reason over multiple potential conditions through iterative questioning to resolve uncertainty. This process requires considering differential diagnoses and actively excluding emergencies that demand immediate intervention. Yet, the ability of medical LLMs to generate informative follow-up questions and thus reason over differential diagnoses remains underexplored. Here, we introduce MedClarify, an AI agent for information-seeking that can generate follow-up questions for iterative reasoning to support diagnostic decision-making. Specifically, MedClarify computes a list of candidate diagnoses analogous to a differential diagnosis, and then proactively generates follow-up questions aimed at reducing diagnostic uncertainty. By selecting the question with the highest expected information gain, MedClarify enables targeted, uncertainty-aware reasoning to improve diagnostic performance. In our experiments, we first demonstrate the limitations of current LLMs in medical reasoning, which often yield multiple, similarly likely diagnoses, especially when patient cases are incomplete or relevant information for diagnosis is missing. We then show that our information-theoretic reasoning approach can generate effective follow-up questioning and thereby reduces diagnostic errors by ~27 percentage points (p.p.) compared to a standard single-shot LLM baseline. Altogether, MedClarify offers a path to improve medical LLMs through agentic information-seeking and to thus promote effective dialogues with medical LLMs that reflect the iterative and uncertain nature of real-world clinical reasoning.

Choosing a Large Language Model (LLM) for a given task requires comparing many strong candidates, yet standard evaluation relies on costly annotations over fixed evaluation sets. To address this challenge, we develop SELECT-LLM, the first framework for active model selection of LLMs. SELECT-LLM aims to find a small set of queries whose annotations are most informative for identifying the best LLM for a given task. To this end, we introduce a query selection rule based on expected information gain, computed from pairwise similarities between candidate model outputs. Because this rule only uses generated model responses, SELECT-LLM can be applied across candidate models without assumptions about their architecture or access to model weights. This makes it suitable for both open-weight and black-box LLMs. We evaluate SELECT-LLM across 23 datasets, 156 evaluated models, diverse task families, and multiple text evaluation metrics. Across all experiments, SELECT-LLM improves over the strongest baseline in every setting, with annotation cost reductions up to 81.8% for best model selection and up to 84.78% for near-best model selection.