This is a comprehensive summary of Reinforcement's lectures, including a number of tips & notes. The summary, like the course, is in English and many formulas have been added.
RL = what to do to maximize a numerical reward
1 action for each situation -> highest reward
Problem of RL:
• Sense of the state of the environment
• Take actions -> affect the state
• Goal relating to the state
Learning from interactions, directly from its environment
Exploration-Exploitation dilemma:
Exploitation: profit from your experience
Exploration: look for better options in the future
Elements of RL:
1. Policy
Behavior of learning agent in time
Action to be taken
Policies may be stochastic
2. Reward Rt
Goal of the problem
Reward-signal
3. Value function V (s)
Total amount of reward expected to accumulate over the future, starting from state s
Long-run desirability of the state, considering future states & rewards
Actions based on value judgements
Value estimation
4. Model environment
Model-free: trial & error learner
Model-based given state & action, model predicts next state & R
→ What action to take as a function of the state signal
→ Learn while interacting
Multi-armed bandits
k-armed bandit → k options & 1 situation: non-associative feedback problem
k: number of actions
t: time step
At: action at t
q* (a): true value of action a (expected reward) = E[Rt | At = a]
q* (a) unknown → We use Qt (a) as an estimation at time t
𝞹
, Action-value methods
Types of actions: Greedy approach: exploiting, so choose a with highest Qt(a)
Exploring actions
= number of times a has been selected until time t
If Nt (a) = 0 , then Qt (a) = c, some default time
If Nt (a) → ♾ , then Qt (a) → q* (a)
Selection:
1. Random selection: P[ At = a ] = 1/k
2. Greedy action selection method At = arg maxa {Qt (a)}
3. -greedy action selection: with prob. select randomly from all actions with equal probability,
otherwise greedy
Offline computing: all data already available : computationally inefficient
Qn = (R1 + … + Rn-1) / (n - 1)
Qn+1 = (R1 + … + Rn-1) / n
Online computing:
new estimate = old estimate + stepwise ( target - old estimate )
Non-stationary: rewards probabilities change over time
give more weight to recent reward than to long-past reward
Varying step-size n (a): convergence for n (a) = 1/2
& no convergence for n (a) = and varying Qn+1
Sample average: bias disappears when actions are selected at least once
Optimistic initial value for Q1(a) → forces to select all options at least once
→ Qt (a) to proper level
𝜺 𝜶 𝜺 𝜶 𝜶 𝜶
, Lecture 2
Observations multi-armed bandits
Optimistic initial value Q1(a):
• Qt+1 = Qn(a) + [Rn(a) - Qn(a)], Q1(a) = c, influence high for small
• Qn+1 = Qn(a) + 1/n [Rn(a) - Qn(a)], whatever Q1(a) = c → Q2(a) = R1(a)
Greedy (with average reward value):
• t > t0 → At = a0, action a0 as long as Qt(a0) > 0 and if q*(a0) > 0
• t→♾ → Qt(a0) → q*(a0), for the ‘absorbing’ action
-Greedy (with average reward value):
• t→♾ → Qt(a) → q*(a), for all actions
• t→♾ → P[At = a*] = ( 1 - ) + / k, with a* = arg maxa {q* (a)}: optimal
Do better by: giving exploiting priority and when we explore:
• Avoid low reward actions (no random selections)
• Good choices for pi: select greedy with high prob. for p1
• Low reward actions will still be selected
Upper-confidence-bound action selection
Explore non-greedy actions with high potential & keep exploring, also in the long-run
Behaviour:
• Sqrt-term measure of uncertainty, like confidence interval
• Value of actions increases in time, even when not selected
• When selected the uncertainty term decreases
• Subtle favoring of less-frequent selected actions
Multi-bandit problem non-associative task: find or track the best action for a single situation (or
state), either stationary or non-stationary
Contextual Bandits
Associative task: find best action for multiple situations (or states), i.e. learn a policy
Associative search: trial-and-error learning and association of actions to situations
Full RL associative task: Actions affect next situation (or state)
𝜺
𝜶 𝜺 𝜺 𝜶
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller feanne1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $12.36. You're not tied to anything after your purchase.