# Questions tagged [multi-armed-bandits]

For questions related to the multi-armed bandit (MAB) problem, in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation.

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### Framing a resource allocation problem without sequential action for Reinforcement Learning

I am attempting to get some insight into framing a resource allocation problem using Reinforcement Learning (RL) where there seem to be no sequential actions (I might be incorrect here). In my ...
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### Should I use multi-armed-bandits or RL for a financial time-series problem?

If we take simple financial timeseries data(stock/commodity/currency prices), State(t+1) does not depend on the action that we choose to take at State(t) as in Maze or Chess problem. Simple example: ...
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1 vote
45 views

### Why will every action be sampled an infinite number of times?

I am reading the book Reinforcement Learning: An Introduction. Second edition (Richard S. Sutton and Andrew G. Barto). In the k-armed bandit problem using $\varepsilon$-greedy selection method, the ...
1 vote
49 views

### References on Theoretical Bandit Problem

I am going to start learning the bandit problem and algorithm, especially how to bound the regret. I found the book Bandit Algorithms'' but it is not easy to follow. It is based on advanced ...
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### References for Stochastic Process for Sequential Decision Making

I am reading papers on Multi-armed bandit problem. In these papers, they use some notations in measure-theory like filtration, adapted filtration, and so on. Also, to prove theorems, many papers ...
• 471
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### UCB algorithm exercise

I am trying to understand the UCB algorithm and I'm trying to understand it using an exercise. Here's the Upper Confidence Bound algorithm explanation: Now I have the following exercise: Suppose we ...
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### Is there a way to form a reward function so that it would take into account the order of the actions?

I want to design a multi-arm bandit system for a multi-step, multi-location system. Locations are dynamic, so I can not design the system based on them. In each location, the alternative actions that ...
1 vote
32 views

### Data Imbalance in Contextual Bandit with Thompson Sampling

I'm working with the Online Logistic Regression Algorithm (Algorithm 3) of Chapelle and Li in their paper, "An Empirical Evaluation of Thompson Sampling" (https://papers.nips.cc/paper/2011/...
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### How to model the probability of click-through in bandit problem?

Consider a bandit problem in which we want to maximize the probability of click-through based on bid values ($b$ is the value of bid and $\Pr(b)$ shows the probability that a customer clicks on a link ...
• 471
1 vote
53 views

### Policy gradient (or more general, RL algorithms) for the problems where actions does not determine next state (next state is independent to action)

I am pretty new in RL. Could anyone suggest results/paper about whether or not policy gradient (or more general RL algorithms) can be applied to the problems where actions does not determine next ...
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1 vote
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### If the probabilities with which each task is selected for you do not change over time, why would it appear as a single stationary k-armed bandit task?

Sutton-Barto (Section 2.9-Associative Search (Contextual Bandits), page 41): As an example, suppose there are several different k-armed bandit tasks, and that on each step you confront one of these ...
• 169
1 vote
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### Gradient bandit algorithm: is $\bar{R}_t$ average of all rewards or average of rewards corresponding to $A_t$?

Sutton-Barto (Section 2.8-Gradient Bandit Algorithms, page 37): Question: is $\bar{R}_t$ average of all rewards or average of rewards corresponding to $A_t$?
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1 vote
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### Can vanilla multi armed bandit problems be solved by RL algorithms like A2C and PPO?

Let's say we have N bandit machines with some distributions (assume some are gaussian, some are uniform, some are chi squared). We want to maximize rewards in X amount of time. I am aware that ...
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### Will adding new arms after every time step still make the problem a Multi Armed Bandit problem?

In Multi Armed Bandit problem, let's say I have 4 arms- {S1, S2, S3, S4}. Each arm has their own probability distribution of rewards. I play the first arm (S1); I get +2 as reward. I add 2 more arms ...
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### Is there a variant of Thompson Sampling that works with variable bandits?

Does there exist a variant of TS, such that, while computing the returns of multi-armed bandits, we have the possibility of introducing an extra bandit? For instance, while we are applying TS to 3 ...
73 views

### Are Best-Arm Bandits considered to be reinforcement learning?

Multi Armed Bandits (MABs) are a broad field of research pursuing different streams. In addition to the common objective of maximizing the cumulative reward, there are also so-called Best-Arm (...
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### Which algorithms work in a non-stationary stochastic environment?

Currently, I am reading into the Multi-Armed-Bandit problem and found the special case of non-stationary (environment and its attributes, like the reward distribution, change over time) stochastic ...
1 vote
75 views

### Is there a paper/article on contextual $\epsilon$-greedy algorithm?

I am reading the paper A Contextual-Bandit Approach to Personalized News Article Recommendation, where it refers to $\epsilon$-greedy (disjoint) algorithm. I suspect, that it is just a version of a K-...
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1 vote
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### Multi-armed Bandit in optimization on graph edges selection

I have the problem, which I described below. I wonder if there exists a class of multi-armed bandit approaches that is related to it. I am working on computer networking optimization. In the simplest ...
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### Is it better to model a Contextual Multi-Armed Bandit problem as an MDP with a non-zero discount factor than treating it as it is?

I'd like to ask if it is, generally, better to model a problem that naturally appears as a Contextual Multi-Armed Bandit like Recommender Systems as a Markov Decision Process with a non-zero discount ...
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1 vote
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### Why do I get bad results no matter my neural network function approximator for parametrized Q-learning implementation for Contextual Bandits?

I'd like to ask you why, no matter my neural network function approximator for parametrized Q-learning implementation for a Contextual Bandits environment, I'm getting bad results. I don't know if it'...
• 509
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### Is the Bandit Problem an MDP?

I've read Sutton and Barto's introductory RL book. They define a policy as a mapping from states to probabilities of selecting each possible action. If the agent is following policy $\pi$ at time $t$, ...
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### What is the probability of selecting the greedy action in a 0.5-greedy selection method for the 2-armed bandit problem?

I'm new to reinforcement learning and I'm going through Sutton and Barto. Exercise 2.1 states the following: In $\varepsilon$-greedy action selection, for the case of two actions and $\varepsilon=0.5$...
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### What are the major differences between multi-armed bandits and the other well-known algorithms (DQN, A3C, PPO, etc)?

I have studied in the past different algorithms, i.e. DQN, DDQN, REINFORCE, A3C, PPO, TRPO, so on. I am doing an internship this summer where I have to use a multi-armed bandit (MAB). I am a bit ...
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### Difference in UCB performance when scaling the rewards

I notice the following behavior when running experiments with $\epsilon$-greedy and UCB1. If the reward is kept binary (0 or 1) both algorithm's performances are on par with each other. However, if I ...
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1 vote
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### Which RL algorithm would be suitable for this multi-dimensional and continuous action space?

Is there an RL approach/algorithm that would be suited for the following kind of problem? There is a continuous action space with an action value $A_{a,t}$ for each action dimension $a$. The ...
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1 vote
128 views

### UCB-like algorithms: how do you compute the exploration bonus?

My question concerns Stochastic Combinatorial Multiarmed Bandits. More specifically, the algorithm called CombUCB1 presented in this paper. It is a UCB-like algorithm. Essentially, in each round of ...
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### In UCB, is the actual upper bound an upper bound of an one-sided or two-sided confidence interval?

I'm a bit confused about the visualization of the upper bound (following the notation of (c.f. Sutton & Barto (2018)) $$Q_t(a)+C\sqrt{\frac{\mathrm{ln}(t)}{N_t(a)}}$$ In many blog posts about the ...
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1 vote
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### How do I learn the value function for a POMDP with a single-step horizon (bandit)?

Consider a POMDP with a finite number of environment states, $|\mathcal{S}| = N$, but the number of belief states is uncountably infinite. The belief state space is the convex hull of an $N$ simplex. ...
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562 views

### Multi Armed Bandits with large number of arms

I'm dealing with a (stochastic) Multi Armed Bandit (MAB) with a large number of arms. Consider a pizza machine that produces a pizza depending on an input $i$ (equivalent to an arm). The (finite) set ...
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1 vote
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### Multi-armed bandit problem without getting rewards

In a 2-armed-bandit problem, an agent has an opportunity to see n reward for each action. Now the agent should choose actions m times and maximize the expected reward in these m decisions. but it cant ...
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286 views

### Why aren't exploration techniques, such as UCB or Thompson sampling, used in full RL problems?

Why aren't exploration techniques, such as UCB or Thompson sampling, typically used in bandit problems, used in full RL problems? Monte Carlo Tree Search may use the above-mentioned methods in its ...
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1 vote
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### Multi-armed bandits: reducing stochastic multi-armed bandits to bernoulli bandits

Agrawal and Goyal (http://proceedings.mlr.press/v23/agrawal12/agrawal12.pdf page 3) discussed how we can extend Thompson sampling for bernoulli bandits to Thompson sampling for stochastic bandits in ...
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### Why do we have two similar action selection strategies for UCB1?

In the literature, there are at least two action selection strategies associated with the UCB1's action selection strategy/policy. For example, in the paper Algorithms for the multi-armed bandit ...
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436 views

### Why is regret so defined in MABs?

Consider a multi-armed bandit(MAB). There are $k$ arms, with reward distributions $R_i$ where $1 \leq i \leq k$. Let $\mu_i$ denote the mean of the $i^{th}$ distribution. If we run the multi-armed ...
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26 views

### Mapping given probabilities to empirical probabilities

Consider following problem statement: You have given $n$ actions. You can perform any of them. Each action gives you success with some probability. The challenge is to perform given finite number of ...
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### Is there a UCB type algorithm for linear stochastic bandit with lasso regression?

Why is there no upper confidence bound algorithm for linear stochastic bandits that uses lasso regression in the case that the regression parameters are sparse in the features? In particular, I don't ...
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1 vote
458 views

### Understanding GLIE conditions for epsilon greedy approach

I was going through this course on reinforcement learning (the course has two lecture videos and corresponding slides) and I had a doubt. On slide 18 of this pdf, it states following condition for an ...
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### Can you convert a MDP problem to a Contextual Multi-Arm Bandits problem?

I'm trying to get a better understanding of Multi-Arm Bandits, Contextual Multi-Arm Bandits and Markov Decision Process. Basically, Multi-Arm Bandits is a special case of Contextual Multi-Arm Bandits ...
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1 vote
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### Customized food for persons based on their profile using Reinforcement learning

I am newbie to Reinforcement Learning, this is my idea - Agent(food provider) has to select a food based on the environment(based on the user profile). Here the reward will be given to the agent based ...
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### Why do we use $X_{I_t,t}$ and $v_{I_t}$ to denote the reward received and the at time step $t$ and the distribution of the chosen arm $I_t$?

I'm doing some introductory research on classical (stochastic) MABs. However, I'm a little confused about the common notation (e.g. in the popular paper of Auer (2002) or Bubeck and Cesa-Bianchi (2012)...
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### Solving multi-armed bandit problems with continuous action space

My problem has a single state and an infinite amount of actions on a certain interval (0,1). After quite some time of googling I found a few paper about an algorithm called zooming algorithm which can ...
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### Why am I getting better performance with Thompson sampling than with UCB or $\epsilon$-greedy in a multi-armed bandit problem? [closed]

I ran a test using 3 strategies for multi-armed bandit: UCB, $\epsilon$-greedy, and Thompson sampling. The results for the rewards I got are as follows: Thompson sampling had the highest average ...
259 views

### How do I recognise a bandit problem?

I'm having difficulty understanding the distinction between a bandit problem and a non-bandit problem. An example of the bandit problem is an agent playing $n$ slot machines with the goal of ...
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### When discounted MAB is useful?

Many of multi-armed bandit(MAB) algorithms are used when the total reward is the sum of all rewards. However, in RL, the discounted reward is mainly used. Why is the discounted reward not prevailing ...
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### Are bandits considered an RL approach?

If a research paper uses multi-armed bandits (either in their standard or contextual form) to solve a particular task, can we say that they solved this task using a reinforcement learning approach? Or ...
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1 vote
271 views

### How do we reach at the formula for UCB action-selection in multi-armed bandit problem?

I came across the formula for Upper Confidence Bound Action Selection (while studying multi-armed bandit problem), which looks like:  A_t \dot{=} \operatorname{argmax}_a \left[ Q_t(a) + c \sqrt{ \...
1 vote
55 views

### How do I determine the optimal policy in a bandit problem with missing contexts?

Suppose I learn an optimal policy $\pi(a|c)$ for a contextual multi-armed bandit problem, where the context $c$ is a composite of multiple context variables $c = c_1, c_2, c_3$. For example, the ...
239 views

### Which solutions could I use to solve a multi-armed "multi-bandit" problem?

Problem I have 66 slot machines. For each of them, I have 7 possible actions/arms to choose from. At each trial, I have to choose one of 7 actions for each and every one of the 66 slots. The reward ...
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