Bayesian optimization is a technique for efficiently optimizing unknown functions in a black-box manner. To handle practical settings where gathering data requires use of finite resources, it is desirable to explicitly incorporate function evaluation costs into Bayesian optimization policies. To understand how to do so, we develop a previously-unexplored connection between cost-aware Bayesian optimization and the Pandora's Box problem, a decision problem from economics. The Pandora's Box problem admits a Bayesian-optimal solution based on an expression called the Gittins index, which can be reinterpreted as an acquisition function. We study the use of this acquisition function for cost-aware Bayesian optimization, and demonstrate empirically that it performs well, particularly in medium-high dimensions. We further show that this performance carries over to classical Bayesian optimization without explicit evaluation costs. Our work constitutes a first step towards integrating techniques from Gittins index theory into Bayesian optimization.

Pandora's Box is a central problem in decision making under uncertainty that can model various real life scenarios. In this problem we are given n boxes, each with a fixed opening cost, and an unknown value drawn from a known distribution, only revealed if we pay the opening cost. Our goal is to find a strategy for opening boxes to minimize the sum of the value selected and the opening cost paid.In this work we revisit Pandora's Box when the value distributions are correlated, first studied in [CGT+20]. We show that the optimal algorithm for the independent case, given by Weitzman's rule, directly works for the correlated case. In fact, our algorithm results in significantly improved approximation guarantees compared to the previous work, while also being substantially simpler. We also show how to implement the rule given only sample access to the correlated distribution of values. Specifically, we find that a number of samples that is polynomial in the number of boxes is sufficient for the algorithm to work.

The Avatar Game Is So Good, They Don't Need to Make the Movies Anymore See the new movie if you'd like. But if you really want to experience the big blue world of Pandora, the video game is where it's at. The Avatar video game is better than the movies. I say this as someone who has dumbly adored James Cameron's Avatar movies for a long time. The original 2009 film was my first ever midnight premiere, which I attended along with a friend who sat in the theater shirtless with his entire body painted blue.

Large reasoning models achieve strong performance on complex tasks by generating extended chains of thought, but they often "overthink": continuing to reason long after they have enough information to answer correctly. This wastes inference-time compute and can hurt accuracy. Existing attempts to stop early either manipulate decoding with extra sampling and heuristics, rely on auxiliary verifier models, or operate only as post-hoc analysis pipelines without formal guarantees. We introduce LYNX, an online early-exit mechanism that turns a model's own hidden-state awareness into confidence-controlled stopping decisions. LYNX attaches exit decisions to naturally occurring reasoning cues (e.g., "hmm", "wait") during generation, trains a lightweight probe on hidden states at those cue tokens using supervision from forced exits, and wraps the resulting scores in split conformal prediction to obtain distribution-free control over premature exits. Crucially, we train and calibrate this probe once on a generic mathematical corpus and reuse it unchanged across benchmarks, decoding temperatures, and even non-mathematical tasks. Across three model families spanning 1.5B to 32B parameters, a single mathematically trained probe per base model yields strong accuracy--efficiency tradeoffs. On GSM8K, LYNX matches or improves baseline accuracy while reducing tokens by 40--65\%; on MATH-500 it improves accuracy by up to 12 points with roughly 35--60\% fewer tokens; on AIME 2024 it recovers baseline accuracy with more than 50\% token savings; and on CommonsenseQA, a non-math benchmark, it transfers zero-shot with modest accuracy gains and up to 70\% fewer tokens. Compared to state-of-the-art early-exit methods, LYNX offers competitive or superior Pareto frontiers while remaining fully online, requiring no proxy models at inference, and providing explicit, user-tunable confidence guarantees.

We evaluate large language models (LLMs) for automatic personality prediction from text under the binary Five Factor Model (BIG5). Five models -- including GPT-4 and lightweight open-source alternatives -- are tested across three heterogeneous datasets (Essays, MyPersonality, Pandora) and two prompting strategies (minimal vs. enriched with linguistic and psychological cues). Enriched prompts reduce invalid outputs and improve class balance, but also introduce a systematic bias toward predicting trait presence. Performance varies substantially: Openness and Agreeableness are relatively easier to detect, while Extraversion and Neuroticism remain challenging. Although open-source models sometimes approach GPT-4 and prior benchmarks, no configuration yields consistently reliable predictions in zero-shot binary settings. Moreover, aggregate metrics such as accuracy and macro-F1 mask significant asymmetries, with per-class recall offering clearer diagnostic value. These findings show that current out-of-the-box LLMs are not yet suitable for APPT, and that careful coordination of prompt design, trait framing, and evaluation metrics is essential for interpretable results.

Gittins index, which can be reinterpreted as an acquisition function.

We can only see the exact value realized in a box if we open it and pay the opening cost.

We study the Pandora's Box problem in an online learning setting with semi-bandit feedback. In each round, the learner sequentially pays to open up to $n$ boxes with unknown reward distributions, observes rewards upon opening, and decides when to stop. The utility of the learner is the maximum observed reward minus the cumulative cost of opened boxes, and the goal is to minimize regret defined as the gap between the cumulative expected utility and that of the optimal policy. We propose a new algorithm that achieves $\widetilde{O}(\sqrt{nT})$ regret after $T$ rounds, which improves the $\widetilde{O}(n\sqrt{T})$ bound of Agarwal et al. [2024] and matches the known lower bound up to logarithmic factors. To better capture real-life applications, we then extend our results to a natural but challenging contextual linear setting, where each box's expected reward is linear in some known but time-varying $d$-dimensional context and the noise distribution is fixed over time. We design an algorithm that learns both the linear function and the noise distributions, achieving $\widetilde{O}(nd\sqrt{T})$ regret. Finally, we show that our techniques also apply to the online Prophet Inequality problem, where the learner must decide immediately whether or not to accept a revealed reward. In both non-contextual and contextual settings, our approach achieves similar improvements and regret bounds.

Personality detection from text aims to infer an individual's personality traits based on linguistic patterns. However, existing machine learning approaches often struggle to capture contextual information spanning multiple posts and tend to fall short in extracting representative and robust features in semantically sparse environments. This paper presents HIPPD, a brain-inspired framework for personality detection that emulates the hierarchical information processing of the human brain. HIPPD utilises a large language model to simulate the cerebral cortex, enabling global semantic reasoning and deep feature abstraction. A dynamic memory module, modelled after the prefrontal cortex, performs adaptive gating and selective retention of critical features, with all adjustments driven by dopaminergic prediction error feedback. Subsequently, a set of specialised lightweight models, emulating the basal ganglia, are dynamically routed via a strict winner-takes-all mechanism to capture the personality-related patterns they are most proficient at recognising. Extensive experiments on the Kaggle and Pandora datasets demonstrate that HIPPD consistently outperforms state-of-the-art baselines.

Gittins index, which can be reinterpreted as an acquisition function.