RECORD
Complexity Analysis of a Countable-armed Bandit Problem
Machine Learning · Submitted 18 Jan 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We study the classical problem of minimizing the expected cumulative regret over a horizon of play $n$, and propose algorithms that achieve a rate-optimal finite-time instance-dependent regret of $\mathcal{O}\left( \log n \right)$.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We consider a stochastic multi-armed bandit (MAB) problem motivated by ``large'' action spaces, and endowed with a population of arms containing exactly $K$ arm-types, each characterized by a distinct mean reward. The decision maker is oblivious to the statistical properties of reward distributions as well as the population-level distribution of different arm-types, and is precluded also from observing the type of an arm after play. We study the classical problem of minimizing the expected cumulative regret over a horizon of play $n$, and propose algorithms that achieve a rate-optimal finite-time instance-dependent regret of $\mathcal{O}\left( \log n \right)$. We also show that the instance-independent (minimax) regret is $\tilde{\mathcal{O}}\left( \sqrt{n} \right)$ when $K=2$. While the order of regret and complexity of the problem suggests a great degree of similarity to the classical MAB problem, properties of the performance bounds and salient aspects of algorithm design are quite distinct from the latter, as are the key primitives that determine complexity along with the analysis tools needed to study them.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider a stochastic multi-armed bandit (MAB) problem motivated by ``large'' action spaces, and endowed with a population of arms containing exactly $K$ arm-types, each characterized by a distinct mean reward. | background 0.95 | 0.27 | 0.04 | asserted 0.97 |
| s1 | The decision maker is oblivious to the statistical properties of reward distributions as well as the population-level distribution of different arm-types, and is precluded also from observing the type of an arm after play. | background 0.97 | 0.12 | 0.02 | asserted 1.00 |
| s2 | We study the classical problem of minimizing the expected cumulative regret over a horizon of play $n$, and propose algorithms that achieve a rate-optimal finite-time instance-dependent regret of $\mathcal{O}\left( \log n \right)$. | contribution 0.66 | 0.94 | 0.70 | asserted 1.00 |
| s3 | We also show that the instance-independent (minimax) regret is $\tilde{\mathcal{O}}\left( \sqrt{n} \right)$ when $K=2$. | result 0.99 | 0.92 | 0.13 | asserted 1.00 |
| s4 | While the order of regret and complexity of the problem suggests a great degree of similarity to the classical MAB problem, properties of the performance bounds and salient aspects of algorithm design are quite distinct from the latter, as are the key primitives that determine complexity along with the analysis tools needed to study them. | interpretation 0.91 | 0.56 | 0.25 | asserted 0.86 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We consider a stochastic multi-armed bandit (MAB) problem motivated by ``large'' action spaces, and endowed with a population of arms containing exactly $K$ arm-types, each characterized by a distinct mean reward. The decision maker is oblivious to the statistical properties of reward distributions as well as the population-level distribution of different arm-types, and is precluded also from observing the type of an arm after play. We study the classical problem of minimizing the expected cumulative regret over a horizon of play $n$, and propose algorithms that achieve a rate-optimal finite-time instance-dependent regret of $\mathcal{O}\left( \log n \right)$. We also show that the instance-independent (minimax) regret is $\tilde{\mathcal{O}}\left( \sqrt{n} \right)$ when $K=2$. While the order of regret and complexity of the problem suggests a great degree of similarity to the classical MAB problem, properties of the performance bounds and salient aspects of algorithm design are quite distinct from the latter, as are the key primitives that determine complexity along with the analysis tools needed to study them.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 1 sentence without a confident label
Cites as background 2 papers
-
Subsequent works have considered more general reward and reservoir distributions on $[0,1]$, see, e.g., [ref] .
Infinite Arms Bandit: Optimality via Confidence Bounds · Introduction · 0.85
-
Lastly, a formulation of the countable-armed problem based on pure exploration, referred to as the “heaviest coin identification problem,” was studied in [ref] for $K=2$ (see [ref] for subsequent developments).
On the Detection of Mixture Distributions with applications to the Most Biased Coin Problem · Introduction · 0.97
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.