# Questions tagged [multi-armed-bandit]

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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### 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'...
36 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 $t$, ...
306 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 ...
81 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 $\varepsilon=0.5$...
88 views

### 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 ...
63 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 ...
75 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 ...
49 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 ...
127 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 ...
87 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 ...
136 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 ...
42 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 ...
66 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 ...
72 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. ...
292 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....
126 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 ...
113 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)...
243 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 ...
27 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 ...
31 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 ...
126 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 ...
68 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{ \...
21 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 ...
25 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 ...
30 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 ...
52 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 ...
415 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 ...
201 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 ...
199 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 ...
37 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 ...
66 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). ...
466 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 ...
220 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 ...