CS 730/730W/830: Intro AI MDP Wrap-Up ADP Q -Learning 1 handout: - - PowerPoint PPT Presentation

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Mar 07, 2023 217 likes •436 views

CS 730/730W/830: Intro AI MDP Wrap-Up ADP Q -Learning 1 handout: slides project proposals are due Wheeler Ruml (UNH) Lecture 18, CS 730 1 / 14 MDP Wrap-Up RTDP MDPs ADP Q -Learning MDP Wrap-Up Wheeler Ruml (UNH) Lecture 18, CS

SLIDE 1

CS 730/730W/830: Intro AI

MDP Wrap-Up ADP Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 1 / 14

1 handout: slides project proposals are due

SLIDE 2

MDP Wrap-Up

MDP Wrap-Up ■ RTDP ■ MDPs ADP Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 2 / 14

SLIDE 3

Real-time Dynamic Programming

MDP Wrap-Up ■ RTDP ■ MDPs ADP Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 3 / 14

for a known MDP. which states to update? initialize U to an upper bound update U as we follow greedy policy from s0 U(s) ← R(s) + γ max

a

s′

T(s, a, s′)U(s′) states that agent is likely to visit (nice anytime profile)

SLIDE 4

Summary of MDP Solving

MDP Wrap-Up ■ RTDP ■ MDPs ADP Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 4 / 14

■

value iteration: compute U π∗

◆

prioritized sweeping

◆

RTDP

■

policy iteration: compute U π using

◆

linear algebra (exact)

◆

simplified value iteration (exact and faster?)

◆

modified PI (a few updates, so inexact)

SLIDE 5

Model-based Reinforcement Learning

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 5 / 14

SLIDE 6

Adaptive Dynamic Programming

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 6 / 14

‘model-based’. active vs passive learn T and R as we go, calculating π using MDP methods (eg, VI or PI) Until max-update ≤ loss − bound (1−γ)2

2γ2

for each state s U(s) ← R(s) + γ maxa

s′ T(s, a, s′)U(s′)

π(s) = argmax

a

s′

T(s, a, s′)U(s′)

SLIDE 7

Prioritized Sweeping

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 7 / 14

given an experience (s, a, s′, r), update model update s repeat k times: do highest priority update to update state s with change δ in U(s): update U(s) priority of s ← 0 for each predecessor s′ of s: priority s′ ← max of current and maxa δ ˆ T(s′, as′)

SLIDE 8

Policy Iteration

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 8 / 14

repeat until π doesn’t change: given π, compute U π(s) for all states given U, calculate policy by one-step look-ahead If π doesn’t change, U doesn’t either. We are at an equilibrium (= optimal π)!

SLIDE 9

Exploration vs Exploitation

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 9 / 14

problem:

SLIDE 10

Exploration vs Exploitation

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 9 / 14

problem: greedy (local minima) U +(s) ← R(s) + γ max

a

f

s′

T(s, a, s′)U +(s′), N(a, s)

where f(u, n) = Rmax if n < k, u otherwise

SLIDE 11

Break

MDP Wrap-Up ADP ■ ADP ■ Sweeping ■ Policy Iteration ■ Bandits ■ Break Q-Learning

Wheeler Ruml (UNH) Lecture 18, CS 730 – 10 / 14

■

asst 4

■

final papers: writing-intensive

SLIDE 12

Model-free Reinforcement Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 11 / 14

SLIDE 13

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′)

SLIDE 14

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′) Q(s, a) = γ

s′
T(s, a, s′)(R(s′) + max

a′

Q(s′, a′))

Given experience s, a, s′, r:

SLIDE 15

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′) Q(s, a) = γ

s′
T(s, a, s′)(R(s′) + max

a′

Q(s′, a′))

Given experience s, a, s′, r:

Q(s, a) ← Q(s, a) + α(error)

SLIDE 16

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′) Q(s, a) = γ

s′
T(s, a, s′)(R(s′) + max

a′

Q(s′, a′))

Given experience s, a, s′, r:

Q(s, a) ← Q(s, a) + α(error) Q(s, a) ← Q(s, a) + α(sensed − predicted)

SLIDE 17

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′) Q(s, a) = γ

s′
T(s, a, s′)(R(s′) + max

a′

Q(s′, a′))

Given experience s, a, s′, r:

Q(s, a) ← Q(s, a) + α(error) Q(s, a) ← Q(s, a) + α(sensed − predicted) Q(s, a) ← Q(s, a) + α(γ(r + max

a′

Q(s′, a′)) − Q(s, a))

SLIDE 18

Q-Learning

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 12 / 14

U(s) = R(s) + γ max

a

s′

T(s, a, s′)U(s′) Q(s, a) = γ

s′
T(s, a, s′)(R(s′) + max

a′

Q(s′, a′))

Given experience s, a, s′, r:

Q(s, a) ← Q(s, a) + α(error) Q(s, a) ← Q(s, a) + α(sensed − predicted) Q(s, a) ← Q(s, a) + α(γ(r + max

a′

Q(s′, a′)) − Q(s, a)) α ≈ 1/N? policy: choose random with probability 1/N?

SLIDE 19

Summary

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs

Wheeler Ruml (UNH) Lecture 18, CS 730 – 13 / 14

Model known (solving MDP):

■

value iteration

■

policy iteration: compute U π using

◆

linear algebra

◆

simplified value iteration

◆

a few updates (modified PI) Model unknown (RL):

■

ADP using

◆

value iteration

◆

a few updates (eg, prioritized sweeping)

■

Q-learning

SLIDE 20

EOLQs

MDP Wrap-Up ADP Q-Learning ■ Q-Learning ■ Summary ■ EOLQs