vault backup: 2024-10-25 09:24:27

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8.md

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+### The 10-arms testbed
+- we compare different strategies to assess the relative effectiveness
+- 10 actions along the X axis
+- Y axis shows the distribution of rewards
+
+-  Each reward is sampled from a normal distribution with some mean q*(a) and variance=1
+- Each q*(a) is drawn from a normal distribution with mean=0 and variance=1
+![[Pasted image 20241025084609.png]]
+
+- q* is randomly sampled from a normal distribution
+- rewards are randomly sampled based on q
+- actions are randomly taken on exploration steps
+- to fairly compare different methods we need to perform many independent run
+- for any learning method we measure its performance over 2000 independent runs
+
+![[Pasted image 20241025084755.png]]
+
+.. add siled ...
+![[Pasted image 20241025084830.png]]
+
+#### Experiments
+- run experiments for different epsilons
+- 0
+- 0.01
+- 0.1
+
+![[Pasted image 20241025084938.png]]
+- exploring more I find the best actions
+- exploring less it will converge slowly
+- not exploring may never find the best action(s)
+
+Let's do the same experiment starting with optimistic initial values
+- we start with a high value for the rewards
+- we set q1(a) = +5 for all actions
+![[Pasted image 20241025085237.png]]
+as we can see, the system explores more at the beginning, which is good as it will find the best actions to take sooner!
+
+**Optimistic initial value method:**
+- explores more at the beginning
+- only effective for stationary problems
+	- for non-stationary problems we have to use eps-greedy
+
+### Optimism in the Face of Uncertainty
+- ...
+- easy problem:
+	- two arms, one always good and one always bad
+	- try both and done
+- hard problem:
+	- arm much better than other one but there is much noise
+	- takes really long time to disambiguate
+
+![[Pasted image 20241025085759.png]]
+which actions should we peek?
+- greedy would peek the green one
+- eps-greedy too
+- optimism in the face of uncertainty says:
+	- the more uncertain we are about an action-value, the more it is to explore that action, as it could turn out to be the best!
+	- principle: *do not take the arm you believe is best, take the one which has the most potential to be the best*
+
+![[Pasted image 20241025090344.png]]
+the brackets represent a confidence interval around q*(a). The system is confident that the value lies somewhere in the region.
+
+If region is very small, we are very certain!
+
+![[Pasted image 20241025090549.png]]
+In this situation we chose Q2 as estimated value is the highest.
+
+#### Action selection
+![[Pasted image 20241025090625.png]]
+... check slides for formula explaination ...
+
+
+- to systematically reduce uncertainity, UCB explores more at the beginning
+- UCB's exploration reduces over time, eps-greedy continues to take a random action 10% of the time
+

q&a.md

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+- explain the problem of energy consumption in sensor networks
+As sensor run on batteries, energy consumption is a serious problem as we want sensors' batteries to last as long as possible. To achieve a low energy consumption is very important to define good MAC and routing strategies.
+For MAC we can use protocols such as S-MAC, allows sensor to sleep most of the time when they are not communicating.
+S-MAC