arXiv Statistics ML

Approximate Universal Prediction under Interaction

arXiv Machine Learning
Oct 22

Learning to Allocate Resources with Censored Feedback

The paper addresses an online resource allocation problem where a budget must be distributed among multiple arms under censored feedback. Each arm yields a reward only if it is activated by an unknown Bernoulli process and the allocated budget exceeds a random threshold from an unknown parametric distribution. The authors establish a worst‑case regret lower bound of Σ(√T), propose the RA‑UCB algorithm achieving near‑optimal regret when the budget is known, and introduce MG‑UCB for unknown, round‑dependent budgets, validating both approaches experimentally.

By Giovanni Montanari, C\^ome Fiegel, Corentin Pla, Aadirupa Saha, Vianney Perchet
arXiv Machine Learning
Oct 22

Approximate Solomonoff Induction: On the Robustness of Learned Universal Predictors

The paper investigates how well practical machine‑learning algorithms approximate Solomonoff’s universal predictor when trained by minimizing log‑loss over diverse datasets. It establishes tight bounds on the worst‑case increase in prediction error caused by approximating the Bayesian mixture predictor, showing that while the excess error can be large in low‑prior environments, it remains bounded on average and under distribution shifts. The authors also extend their analysis to finite‑sample settings relevant to neural networks and Transformers.

By Qian Li, Shang-Hua Teng
arXiv Machine Learning
Sep 17

A Convergence Framework for Deep $V$-Learning: Error Propagation and Sharp Action-Gap Bounds

The paper presents a convergence framework for deep $V$‑learning over a finite horizon $H$, deriving explicit bounds on policy loss by decomposing the Bellman update error into six residuals. It shows how $L^s$ concentrability controls expected $L^1$ loss, quantifies the impact of shared sampling across horizon levels, and provides optimal and near‑optimal sample allocations for statistical error rates. The work also establishes sharp action‑gap bounds under a margin condition, transfers optimal‑gap results to frozen‑iterate gaps, and offers consistency guarantees for generative‑reset approximate‑ERM procedures with exact action scores.

By Yury Kolomeytsev
arXiv AI
Sep 25

Certified Task-Conditioned Active Observability

The paper introduces the concept of task‑conditioned active observability, defining the minimal interaction cost needed for an autonomous agent to identify task‑relevant states while guaranteeing safe abstention. It formalizes this complexity, proving that task‑predictive equivalence yields a unique minimal sufficient quotient that preserves complexity and eliminates unnecessary distinctions. The authors present theoretical characterizations for deterministic and noisy regimes, and demonstrate a certified observer that reduces sensor usage and model steps while maintaining zero false acceptances in extensive high‑dimensional trials.

By Linzhe Zhang, Changming Xu
arXiv AI
1d ago

Satisficing as competitive Bayesian weighting: a minimal model of goal-directed choice under an unattained target

The paper introduces Risk‑Sensitive Satisficing (RS), a bandit learning rule that evaluates actions based on their past frequency and their surplus or shortfall relative to an aspiration level. RS can be reformulated as Attention Competitive Bayes (ACB), a Bayesian‑like estimator where the aspiration level serves as a prior mean and the limited number of trials limits how strongly evidence can override this prior. ACB predicts that unchosen actions gradually revert toward the aspiration level (pseudo‑forgetting) and that when the aspiration is unattainable, exploration never fully settles, reducing regret in simulations.

By Moto Shinriki, Yu Kono, Tatsuji Takahashi