Passbandit

Passbandit is a term used in the study of sequential decision making to describe a bandit-style problem in which the feedback signal is filtered by a passband. The concept blends ideas from the multi-armed bandit framework with a signal-processing view of observations: rewards (or sensing signals) are subject to a frequency-domain filter that passes only components within a specified frequency range and attenuates others. In this formulation, at each time step the agent selects an action from a finite set, and the observed reward is the output of a latent stochastic process that is assumed to be band-limited in time. The observed reward may be the filtered version of the latent reward, introducing temporal correlations and potential non-stationarity into the feedback.

Formulations of the passbandit problem generally consider whether the filter is known or unknown, and whether the latent process is stationary or non-stationary. Some models assume a linear, time-invariant filter with a known impulse response, while others treat the filter as part of the unknown environment. The central objective remains to maximize cumulative reward over time, but the presence of a passband complicates exploration-exploitation strategies due to correlated observations and reduced information per time step.

Algorithmic approaches to passbandit adapt classical bandit methods to account for filtering effects. Techniques include incorporating deconvolution or state-space models to estimate latent rewards, employing Thompson sampling or UCB variants with priors or filters over latent signals, and using frequency-domain features to guide action selection. Applications discussed in the literature include wireless communications, cognitive radio, and adaptive sensing, where observations are naturally filtered by channel or sensor bandwidth.

See also: multi-armed bandit, contextual bandits, Thompson sampling, Kalman filtering, signal processing.