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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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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 ...
notaprogrammertoday's user avatar
6 votes
1 answer
3k views

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 $\varepsilon=0.5$...
Daviiid's user avatar
  • 575
6 votes
1 answer
338 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 ...
blue-sky's user avatar
  • 335
6 votes
1 answer
524 views

What is a weighted average in a non-stationary k-armed bandit problem?

In the book Reinforcement Learning: An Introduction (page 25), by Richard S. Sutton and Andrew G. Barto, there is a discussion of the k-armed bandit problem, where the expected reward from the bandits ...
chessprogrammer's user avatar
5 votes
2 answers
2k views

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 ...
user5093249's user avatar
5 votes
1 answer
1k views

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 ...
peidaqi's user avatar
  • 151
5 votes
1 answer
379 views

It is possible to solve a problem with continuous action spaces and no states with reinforcement learning?

I want to use Reinforcement Learning to optimize the distribution of energy for a peak shaving problem given by a thermodynamical simulation. However, I am not sure how to proceed as the action space ...
FS93's user avatar
  • 145
5 votes
1 answer
859 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 ...
D. B.'s user avatar
  • 101
4 votes
2 answers
779 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 ...
stoic-santiago's user avatar
4 votes
2 answers
120 views

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)...
MAB_N00B's user avatar
4 votes
1 answer
558 views

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 ...
nbro's user avatar
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4 votes
1 answer
728 views

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 $t$, ...
Snowball's user avatar
  • 225
3 votes
3 answers
702 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 ...
Mika's user avatar
  • 341
3 votes
1 answer
686 views

How to implement a contextual reinforcement learning model?

In a reinforcement learning model, states depend on the previous actions chosen. In the case in which some of the states -but not all- are fully independent of the actions -but still obviously ...
freesoul's user avatar
  • 246
3 votes
0 answers
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 ...
Rnj's user avatar
  • 221
2 votes
1 answer
89 views

Programming a bandit to optimize donations

I'm developing a multi-armed bandit which learns the best information to display to persuade someone to donate to charity. Suppose I have treatments A, B, C, D (which are each one paragraph of text). ...
wwl's user avatar
  • 153
2 votes
1 answer
61 views

Is it possible to describe wordle as a multi armed bandit problem?

Game wordle got fame in January 2022 on Twitter (now knows as X). Rules are pretty simple. Player has to guess a word of length 5 Player can make at most 6 guesses ...
Bhavesh Achhada's user avatar
2 votes
1 answer
225 views

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 $A_t$?
user3489173's user avatar
2 votes
1 answer
340 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 ...
FS93's user avatar
  • 145
2 votes
1 answer
68 views

UCB, Thompson sampling etc seems myopic/greedy for bandits?

When considering multi-armed bandits in different formats, UCB, $\epsilon$-greedy, thompson sampling etc seems so greedy/myopic in the sense that it solely considers reward for the current timestep. ...
hugh's user avatar
  • 53
2 votes
1 answer
580 views

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 ...
d56's user avatar
  • 243
2 votes
1 answer
488 views

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 ...
D. B.'s user avatar
  • 101
2 votes
0 answers
128 views

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 ...
Daviiid's user avatar
  • 575
2 votes
0 answers
57 views

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 ...
lighting's user avatar
  • 121
2 votes
0 answers
88 views

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 ...
PJORR's user avatar
  • 21
2 votes
0 answers
164 views

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 ...
Peter's user avatar
  • 21
1 vote
1 answer
120 views

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'...
Daviiid's user avatar
  • 575
1 vote
1 answer
3k views

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 ...
Java coder's user avatar
1 vote
1 answer
546 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{ \...
SAGALPREET SINGH's user avatar
1 vote
1 answer
570 views

Why is it useful in some applications to use features that are shared by all arms?

In Li et al. (2010)'s highly cited paper, they talk about LinUCB with hybrid linear models in Section 3.2. They motivate this by saying In many applications including ours, it is helpful to use ...
wwl's user avatar
  • 153
1 vote
1 answer
351 views

How can I incorporate domain knowledge to choose actions in the case of large action spaces in multi-armed bandits?

Suppose one is using a multi-armed bandit, and one has relatively few "pulls" (i.e. timesteps) relative to the action set. For example, maybe there are 200 timesteps and 100 possible actions....
wwl's user avatar
  • 153
1 vote
1 answer
110 views

Is it true that a multi-armed-bandit selects an action based on the future reward?

During my machine learning lecture I saw the following statement on the slides: "Multi-armed-bandit selects an action based on the future reward" Is that statement true? In my opinion it is ...
max0r's user avatar
  • 13
1 vote
1 answer
55 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 ...
k2pctdn's user avatar
  • 55
1 vote
1 answer
65 views

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 ...
user3489173's user avatar
1 vote
1 answer
201 views

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 ...
Amin's user avatar
  • 481
1 vote
0 answers
51 views

Python libraries for mulit-armed bandit problems [closed]

I am working on a problem that can be casted as a contextual bandit problem with continuous action space. I would like to tackle it by using something like the contextual zooming algorithm from the ...
Onil90's user avatar
  • 183
1 vote
2 answers
100 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 ...
Amin's user avatar
  • 481
1 vote
0 answers
50 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/...
MABQ's user avatar
  • 11
1 vote
0 answers
64 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 ...
Penn's user avatar
  • 11
1 vote
0 answers
83 views

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 ...
Prasanjit Rath's user avatar
1 vote
0 answers
112 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-...
d56's user avatar
  • 243
1 vote
0 answers
58 views

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 ...
Ramon's user avatar
  • 21
1 vote
0 answers
100 views

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 ...
shimeji42's user avatar
  • 111
1 vote
0 answers
241 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 ...
Adam's user avatar
  • 11
1 vote
0 answers
95 views

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. ...
jdizzle's user avatar
  • 61
1 vote
0 answers
43 views

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 ...
Felix P.'s user avatar
  • 297
1 vote
0 answers
802 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 ...
Mahesha999's user avatar
1 vote
0 answers
32 views

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 ...
Bala u1's user avatar
  • 11
1 vote
0 answers
73 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 ...
user31663's user avatar
1 vote
0 answers
34 views

Name of a multiarmed bandit with only some levers available

In order to model a card game, as an exercise, I was thinking of an elementary setting as a multiarmed bandit, each lever being the distribution of expected rewards of a specific card. But, of course,...
arivero's user avatar
  • 51