Questions tagged [upper-confidence-bound]

For questions about the upper confidence bound (UCB)-based algorithms or action selection strategies in the context e.g. of bandit or reinforcement learning problems.

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How UCT in MCTS selection phase avoids starvation?

The first step of MCTS is to keep choosing nodes based on Upper Confidence Bound applied to trees (UCT) until it reaches a leaf node where UCT is defined as $$\frac{w_i}{n_i}+c\sqrt{\frac{ln(t)}{n_i}},...
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0answers
33 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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1answer
25 views

What should the initial UCT value be with MCTS, when leaf's simulation count is zero? Infinity?

I am implenting a Monte Carlo Tree Search algorithm, where the selection process is done through Upper Confidence Bound formula: ...
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1answer
55 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 ...
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1answer
215 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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0answers
34 views

Why is the ideal exploration parameter in the UCT algorithm $\sqrt{2}$?

From Wikipedia, in the Monte-Carlo Tree Search algorithm, you should choose the node that maximizes the value: $${\displaystyle {\frac {w_{i}}{n_{i}}}+c{\sqrt {\frac {\ln N_{i}}{n_{i}}}}},$$ where ${...
2
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3answers
78 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 ...
2
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1answer
111 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 ...
5
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2answers
110 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)...
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1answer
197 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 ...
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2answers
90 views

Should I use exploration strategy in Policy Gradient algorithms?

In policy gradient algorithms the output is a stochastic policy - a probability for each action. I believe that if I follow the policy (sample an action from the policy) I make use of exploration ...
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1answer
60 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{ \...