Organizations increasingly rely on sequential experimentation to improve decision-making. While the multi-armed bandit literature has developed algorithms with strong asymptotic regret guarantees, many practical applications operate over finite and externally imposed horizons. Motivated by the finite-horizon setting, we develop a class of regularized greedy algorithms for multi-armed Bernoulli bandits. We derive the first finite-horizon regret envelopes for regularized greedy bandits, showing that finite-horizon regret decomposes into transient exploration costs and a suboptimal convergence term that decays exponentially with the regularization strength. This characterization yields principled calibration rules for the regularization parameters and, as a limiting case, sharper regret guarantees for the classical greedy policy. Across extensive numerical experiments, calibrated regularized greedy policies consistently match or outperform state-of-the-art algorithms. These results suggest that regularized greedy policies can provide an effective approach for finite-horizon bandit problems.
We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$. We propose a new algorithm and prove a regret upper bound \[\tilde O(\sqrt{SA…
Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle. We frame AIF as policy optimization and show that, for closed-loop control policies, EFE minimiza…
Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium. We study this regime under a contractive fast map and a non-expansive reduced slow map. We first pr…
Observational causal analyses increasingly pool records across sites, vendors, and collection systems, creating vulnerability to append-only attacks in which plausible records are strategically selected to alter a reported treatment effect. We develop a data-poisoning audit for a…
We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and n…
Many online decision-making problems involve both round-specific feasible actions and drifting reward models: eligible ad impressions, feasible prices, and available treatments can change over time, while user preferences, demand curves, and patient responses may evolve. Motivate…