Podcast
Questions and Answers
What is the conditional probability of B given A?
What is the conditional probability of B given A?
When can we say P(B|A)=P(B)?
When can we say P(B|A)=P(B)?
What is the value of P(A and B) if P(B|A) = 0.5 and P(A) = 0.8?
What is the value of P(A and B) if P(B|A) = 0.5 and P(A) = 0.8?
What is the conditional probability of drawing another red ball given that a red ball has been drawn and kept?
What is the conditional probability of drawing another red ball given that a red ball has been drawn and kept?
Signup and view all the answers
Which of the following statements is TRUE about the conditional probability of B given A?
Which of the following statements is TRUE about the conditional probability of B given A?
Signup and view all the answers
What is the optimal value function for node 'A'?
What is the optimal value function for node 'A'?
Signup and view all the answers
Which node has the highest optimal value function?
Which node has the highest optimal value function?
Signup and view all the answers
Which node is the starting point of the optimal path to 'J'?
Which node is the starting point of the optimal path to 'J'?
Signup and view all the answers
What optimal path does the equation "max{6+V(B), 1+V(C), 2+V(D)} = 16" represent for node 'A'?
What optimal path does the equation "max{6+V(B), 1+V(C), 2+V(D)} = 16" represent for node 'A'?
Signup and view all the answers
What is the value of 'V(B)'?
What is the value of 'V(B)'?
Signup and view all the answers
What is the meaning of "Optimal Path" in this context?
What is the meaning of "Optimal Path" in this context?
Signup and view all the answers
What is the optimal path for node 'C'?
What is the optimal path for node 'C'?
Signup and view all the answers
What is the highest reward that can be obtained from node 'H' to 'J'?
What is the highest reward that can be obtained from node 'H' to 'J'?
Signup and view all the answers
What is the optimal path that leads to a total reward of 14?
What is the optimal path that leads to a total reward of 14?
Signup and view all the answers
Which node has an optimal value function of 8?
Which node has an optimal value function of 8?
Signup and view all the answers
Is it true that in a constant environment, there is only one optimal action for a given state?
Is it true that in a constant environment, there is only one optimal action for a given state?
Signup and view all the answers
When maximizing rewards, which action is considered the best?
When maximizing rewards, which action is considered the best?
Signup and view all the answers
In the context of reinforcement learning, what characterizes the actions in the generalizing scenario?
In the context of reinforcement learning, what characterizes the actions in the generalizing scenario?
Signup and view all the answers
Which statement about the actions in deterministic environments is correct?
Which statement about the actions in deterministic environments is correct?
Signup and view all the answers
What is the significance of state rewards in a reinforcement learning context?
What is the significance of state rewards in a reinforcement learning context?
Signup and view all the answers
What does the minimax algorithm assume about the opponent's behavior?
What does the minimax algorithm assume about the opponent's behavior?
Signup and view all the answers
Which element is essential for applying dynamic programming to compute an optimal solution?
Which element is essential for applying dynamic programming to compute an optimal solution?
Signup and view all the answers
What scores does the minimax algorithm assign for game outcomes?
What scores does the minimax algorithm assign for game outcomes?
Signup and view all the answers
What is the optimal path from node B to node J given that $V(H) = 3$, $V(I) = 4$ and $V(J) = 0$?
What is the optimal path from node B to node J given that $V(H) = 3$, $V(I) = 4$ and $V(J) = 0$?
Signup and view all the answers
In a minimax scenario, which move would X choose?
In a minimax scenario, which move would X choose?
Signup and view all the answers
What is a characteristic of reinforcement learning agents?
What is a characteristic of reinforcement learning agents?
Signup and view all the answers
What is the value of V(D) when k=2, given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
What is the value of V(D) when k=2, given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
Signup and view all the answers
What best describes the goal of minimax in a two-player game?
What best describes the goal of minimax in a two-player game?
Signup and view all the answers
When k=4 and considering a maximum reward calculation, why does the value of V(D) change between page 27 and page 29?
When k=4 and considering a maximum reward calculation, why does the value of V(D) change between page 27 and page 29?
Signup and view all the answers
How does the value of V(B) change between the dynamic programming approach and the Bellman equation approach when k = 0?
How does the value of V(B) change between the dynamic programming approach and the Bellman equation approach when k = 0?
Signup and view all the answers
How does a reinforcement learning agent interact with its environment?
How does a reinforcement learning agent interact with its environment?
Signup and view all the answers
What is the optimal path from node A to node J when $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$??
What is the optimal path from node A to node J when $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$??
Signup and view all the answers
Why is a lookup table beneficial in the context of minimax?
Why is a lookup table beneficial in the context of minimax?
Signup and view all the answers
What is the value of $V(B)$ when $V(E) = 5$, $V(F) = 5$, and $V(G) = 5$?
What is the value of $V(B)$ when $V(E) = 5$, $V(F) = 5$, and $V(G) = 5$?
Signup and view all the answers
What is the optimal path from node A to J given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
What is the optimal path from node A to J given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
Signup and view all the answers
What is the maximum reward that can be achieved from node B to J given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
What is the maximum reward that can be achieved from node B to J given that $V(H) = 1$, $V(I) = 1$ and $V(J) = 0$?
Signup and view all the answers
What is the meaning of the symbol "k" in the given diagrams?
What is the meaning of the symbol "k" in the given diagrams?
Signup and view all the answers
How does the Bellman equation approach differ from the dynamic programming approach in calculating the maximum reward from node A to node J?
How does the Bellman equation approach differ from the dynamic programming approach in calculating the maximum reward from node A to node J?
Signup and view all the answers
On page 27, what is the value of $V(D)$ given that $V(E) = 4$, $V(F) = 7$ and $V(G) = 6$?
On page 27, what is the value of $V(D)$ given that $V(E) = 4$, $V(F) = 7$ and $V(G) = 6$?
Signup and view all the answers
Consider the calculation of $V(A)$ on page 27. What is the maximum reward achievable from node A to node J given that $V(B) = 11$, $V(C) = 7$ and $V(D) = 8$?
Consider the calculation of $V(A)$ on page 27. What is the maximum reward achievable from node A to node J given that $V(B) = 11$, $V(C) = 7$ and $V(D) = 8$?
Signup and view all the answers
If we change $V(H)$ to 0 on page 26, what is the optimal path from node B to node J?
If we change $V(H)$ to 0 on page 26, what is the optimal path from node B to node J?
Signup and view all the answers
On page 28, what is the value of $V(C)$ given that $V(E) = 5$, $V(F) = 5$, and $V(G) = 5$?
On page 28, what is the value of $V(C)$ given that $V(E) = 5$, $V(F) = 5$, and $V(G) = 5$?
Signup and view all the answers
What does the function Q(xk, uk) represent in the context of the Simple MDP?
What does the function Q(xk, uk) represent in the context of the Simple MDP?
Signup and view all the answers
Which action taken in state x=1 leads to state x=2?
Which action taken in state x=1 leads to state x=2?
Signup and view all the answers
What is the value of R(xk, uk) for action u0 in state x=1?
What is the value of R(xk, uk) for action u0 in state x=1?
Signup and view all the answers
Given the transition matrix, what is the next state after action uccw from state x=0?
Given the transition matrix, what is the next state after action uccw from state x=0?
Signup and view all the answers
What does V(xk+1) denote in the equation Q(xk, uk)?
What does V(xk+1) denote in the equation Q(xk, uk)?
Signup and view all the answers
What is the result of the equation Q(xk, uk) when using R(xk, uk) and V(xk+1)?
What is the result of the equation Q(xk, uk) when using R(xk, uk) and V(xk+1)?
Signup and view all the answers
If the reward R(xk, ucw) for state x=0 is 2, what is the corresponding value of Q(xk, ucw)?
If the reward R(xk, ucw) for state x=0 is 2, what is the corresponding value of Q(xk, ucw)?
Signup and view all the answers
What are the possible actions in state x=2 based on the provided transition matrix?
What are the possible actions in state x=2 based on the provided transition matrix?
Signup and view all the answers
For action ucw in state x=1, what is the next state?
For action ucw in state x=1, what is the next state?
Signup and view all the answers
If the V(x=1) is calculated as 8, what is the effect on Q(xk, u0) for state x=1 using R(xk, u0)?
If the V(x=1) is calculated as 8, what is the effect on Q(xk, u0) for state x=1 using R(xk, u0)?
Signup and view all the answers
What is the reward associated with action uccw in state x=2?
What is the reward associated with action uccw in state x=2?
Signup and view all the answers
Which state can be reached by taking action u0 in state x=0?
Which state can be reached by taking action u0 in state x=0?
Signup and view all the answers
What role does the matrix adj(xk, uk) play in the MDP?
What role does the matrix adj(xk, uk) play in the MDP?
Signup and view all the answers
The maximum reward obtained from action u0 in state x=2 is?
The maximum reward obtained from action u0 in state x=2 is?
Signup and view all the answers
Flashcards
Conditional Probability
Conditional Probability
The probability of event B occurring given that event A has already occurred.
Independence in Probability
Independence in Probability
Two events A and B are independent if the occurrence of A does not affect the probability of B.
Bayes’s Rule
Bayes’s Rule
A formula for finding a conditional probability, showing how to update the probability of B based on the occurrence of A.
Drawing Balls without Replacement
Drawing Balls without Replacement
Signup and view all the flashcards
Joint Probability
Joint Probability
Signup and view all the flashcards
Optimal Action
Optimal Action
Signup and view all the flashcards
Q Value
Q Value
Signup and view all the flashcards
Deterministic
Deterministic
Signup and view all the flashcards
State Rewards
State Rewards
Signup and view all the flashcards
Action Horizon
Action Horizon
Signup and view all the flashcards
Sequential Decision Problem
Sequential Decision Problem
Signup and view all the flashcards
Minimax
Minimax
Signup and view all the flashcards
Zero-Sum Game
Zero-Sum Game
Signup and view all the flashcards
Optimal Move
Optimal Move
Signup and view all the flashcards
Reinforcement Learning
Reinforcement Learning
Signup and view all the flashcards
Game State
Game State
Signup and view all the flashcards
Lookup Table
Lookup Table
Signup and view all the flashcards
Opponent Model
Opponent Model
Signup and view all the flashcards
Dynamic Programming
Dynamic Programming
Signup and view all the flashcards
Optimal Path
Optimal Path
Signup and view all the flashcards
Maximal Reward
Maximal Reward
Signup and view all the flashcards
State J
State J
Signup and view all the flashcards
State H
State H
Signup and view all the flashcards
State I
State I
Signup and view all the flashcards
Future Rewards
Future Rewards
Signup and view all the flashcards
Greedy Approach
Greedy Approach
Signup and view all the flashcards
Max Operator
Max Operator
Signup and view all the flashcards
Bellman's Principle
Bellman's Principle
Signup and view all the flashcards
Value Function V(x)
Value Function V(x)
Signup and view all the flashcards
Min Operator
Min Operator
Signup and view all the flashcards
Action Chain
Action Chain
Signup and view all the flashcards
State B
State B
Signup and view all the flashcards
State Transition
State Transition
Signup and view all the flashcards
Action Notation
Action Notation
Signup and view all the flashcards
Adjacency Matrix
Adjacency Matrix
Signup and view all the flashcards
Reward Function R
Reward Function R
Signup and view all the flashcards
Value Function V
Value Function V
Signup and view all the flashcards
Computing Q(xk)
Computing Q(xk)
Signup and view all the flashcards
Transition Dynamics
Transition Dynamics
Signup and view all the flashcards
Cost Function
Cost Function
Signup and view all the flashcards
Markov Decision Process (MDP)
Markov Decision Process (MDP)
Signup and view all the flashcards
State Representation
State Representation
Signup and view all the flashcards
Action Space
Action Space
Signup and view all the flashcards
Feedback Loop
Feedback Loop
Signup and view all the flashcards
Decision Points
Decision Points
Signup and view all the flashcards
Backward Steps
Backward Steps
Signup and view all the flashcards
Action
Action
Signup and view all the flashcards
Maximum Function
Maximum Function
Signup and view all the flashcards
Policy
Policy
Signup and view all the flashcards
Cumulative Reward
Cumulative Reward
Signup and view all the flashcards
J State
J State
Signup and view all the flashcards
H State
H State
Signup and view all the flashcards
Pathfinding
Pathfinding
Signup and view all the flashcards
Optimal Policy
Optimal Policy
Signup and view all the flashcards
Study Notes
Reinforcement Learning for Control and Design Optimization
- This presentation covers reinforcement learning (RL) concepts, including basic terms and elements of RL, different RL algorithms, distinctions between RL and control, and RL applications in design optimization.
- Learning objectives for the lecture include understanding RL, basic RL terms, RL algorithm types, distinguishing RL from control, and comprehending RL's role in design optimization.
- The course is delivered with two lectures and two tutorials every week, and the lecturers are Bojana Rosic and Mark Vlutters as well as Wouter Schuttert, and Vasos Arnaoutis for the tutorials
Reinforcement Learning Concepts/History
- Reinforcement learning was introduced by Pavlov in 1903.
- Reinforcement describes the strengthening of association between an unconditioned stimulus (e.g., food) and a conditioned stimulus (e.g., bell) that results when these two are presented together.
- This eventually leads to a conditioned response, such as salivation by a dog when it only hears the bell.
- Edward Thorndike (1898) further developed the idea with experiments involving cats and a puzzle box, establishing the "Law of Effect". This law suggests that actions with positive outcomes are more likely to be repeated, whereas those with negative outcomes are less likely.
Reinforcement Learning for Engineering
- Reinforcement learning is not restricted to two-person games. It can also be applied in "games against nature".
- RL is applicable in scenarios with discrete or continuous states.
- The principle behind RL involves agents that explore and interact with their environment through trial and error, receiving rewards or penalties for their actions.
- The goal is to maximize cumulative reward over time.
- Essential elements of reinforcement learning include an agent, action, environment, reward, the policy (that maps state to action), and current state.
- RL relies on a combination of exploration (trying unproven actions) and exploitation, (using previously successful actions)
- RL methods can be broadly categorized into Model-Based and Model-Free RL.
RL Elements
- Environment: The external world in which the learning agent exists.
- State: The current configuration or conditions of the environment observed by the agent.
- Action: The action taken by the agent, which changes the state and possibly yields a reward.
- Reward: The signal indicating the outcome of an action; A numerical feedback.
- Policy: A strategy that maps states to actions the agent should take.
- Agent: The entity within the environment that determines actions given the current state.
Reinforcement Learning vs. Control
- Reinforcement learning maximizes the value of states, while optimal control minimizes the cost of states.
- In RL, the environment is often considered a black box.
- In contrast, control may utilize a known model of the system's dynamics and can calculate the optimal control policies.
RL for Optimal Design
- Optimal Truss design is a multi-objective optimization problem involving minimum volume and maximum stress endurance.
- Key elements include the minimization of volume and the maximization of stress endurance.
RL Goals
- The primary goal involves creating an autonomous agent, with the ability to maximize cumulative reward in a given environment.
- Using elements like Markov reward processes and defining state value as the total cumulative reward over the future starting from that state, an optimal policy can be calculated.
RL Classification
- The lecture covers various RL algorithms.
- RL is often categorized into model-based and model-free learning methods.
- Model-based RL methods are preferred when the model of the environment is known.
- Model-free methods are used when an environment model is unknown or too complex to characterize explicitly.
Tic-Tac-Toe
- A two-player zero-sum game where each player knows all possible opponent actions and the objective values of the game states are opposite numbers.
- The goal is to select the optimal move while assuming the opponent is also acting optimally. - Minimax search can find optimal moves in such games by pre-computing the best move for each game state.
Minimax
- A decision strategy for two-player zero-sum games.
- The goal is to choose the best move assuming the opponent is also acting optimally.
- Intermediate scoring involves consistently assessing the opposing player's moves and picking the best action according to those evaluations.
RL Learning Strategies
- Model-based Reinforcement Learning: Use a model of the environment to predict future states and rewards.
- Model-free Reinforcement Learning: Learn a policy or Q-function directly from interactions with an environment, without a model of it. (e.g., Monte-Carlo Methods, temporal-difference methods (e.g., SARSA and Q-learning))
Reinforcement Learning (RL) and Games
- Reinforcement learning is often applied to games, such as Tic-Tac-Toe, to assess and analyze patterns and strategies employed by the opponent to optimize the outcome.
RL Elements Extended
- A policy maps states to actions the agent should take.
- Policies define the agent's rules and actions in a specific state.
- Reinforcement learning is a method where an agent learns a policy (decision-making strategy) through trial and error in a dynamic environment.
Exploration and Exploitation
- Exploitation refers to using the knowledge agent has accrued based on past interactions to select actions likely to yield high rewards.
- Exploration is the strategy of trying out less well-known or novel actions to discover potentially better strategies for maximizing cumulative reward.
Function Approximation
-
This may be employed in RL because the state and action space might be too large or the relationship between state variables and actions might be too complex for tabular representation.
-
Neural Networks can approximate complex functions, adapting well to complex tasks and large state/action spaces.
Gradient Descent
-
Gradient descent is essential for learning in reinforcement learning, especially when function approximation is employed.
-
The gradient of a loss/error function indicates the direction in which the parameters should be adjusted to reduce the loss/error.
Markov Reward Process
- It represents a Markov chain with a reward function.
- A key element used to quantitatively model and represent sequential decision problems in Reinforcement Learning (RL).
- It describes how actions lead to states and the immediate outcomes (rewards) that result.
Markov Decision Processes (MDPs)
- It mathematically models decision processes in sequential environments
- An integral component in both dynamic programming (DP) and some machine learning methods.
- It specifies the world states, the agent's available movements, and the potential outcomes (rewards) of different actions.
Markov Chain Process
- Probability of the current state only depends on the preceding state and independent from earlier states. This "memorylessness" enables more efficient analyses.
- The transition from one state to the next only depends on the current state, with no memory of previous states.
- This Markov property allows algorithms to focus on current circumstances without tracking past history.
Q-Learning (Off-Policy TD Control)
- Used to estimate π, which determines the optimal policy in a given state.
- Q-learning does not necessitate a model of the environment to learn the optimal policy.
REINFORCE (MC-Policy Gradient Control)
- An iterative procedure to estimate a good policy in a given environment when no system model is available.
- It enables learning of a policy that directly maximizes the expected return.
How to Select Actions in an Environment
- Agents can adopt various strategies and procedures when selecting actions.
- Exploration strategies encompass evaluating various choices, while exploitation strategies leverage established patterns to choose the actions.
- Decision selection considerations include how much weight the agent should place on potentially improving its reward vs exploring unfamiliar choices.
Stochastic Environments
- Agents learn the optimal policy under uncertainty about future states.
- The action taken is not always guaranteed to result in the same future state(s), and the resulting rewards are likewise not certain.
Off-policy Learning
-
This approach enables learning for a target policy while using another (behavior) policy to collect the required information.
-
An agent can estimate its evaluation (Q-value) based on actions under a different strategy (behavior policy).
-
This can be useful when the goal policy is unsuitable for exploration, or when learning about the environment's potential actions.
-
Weighted Importance Sampling
-
This technique computes the expected returns from different policies, taking into account the differences in the various policies' probability of selecting an action at any given state.
-
This technique enables learning of the target policy through sample averages, even when using a behavior policy different from what is desired.
Practical Applications of RL
-
These techniques find varied applications within various domains, like robotics.
-
The development of robot navigation strategies and other forms of robot control, allowing robots to learn to interact with environments and accomplish tasks autonomously.
Generalizing over States
- In certain reinforcement learning frameworks, there may be challenges in generalizing agent behavior learned in one situation to new and different states.
Multi-Agent RL and Game Theory
- A key concept and strategy for analyzing multi-agent systems, involving the interactions between multiple agents within an environment.
Challenges of Multi-Agent RL
-
The difficulty of determining the credit assignment problem. (i.e. how do we evaluate which agent's actions contributed to the end outcome effectively)
-
The computational complexity of training increases with the number of agents.
-
The nature of the environment and the relationships between agents influence the learning process and the optimal strategies
Markov Games
- Formally defines multi-agent environments within decision-making frameworks.
- It describes different models for varied interaction types among agents, such as competitive or cooperative situations.
Learning Methods in Multi-Agent RL
-
Centralized training and execution (CTE) involves a unified controller to guide the learning and performance of all agents.
-
Decentralized training and execution (DTE) allows each agent to learn its strategy independently.
Markov Reward Process in Multiple Agents
- The structure of the environment influences the possible outcomes (rewards/penalties) obtained with different actions from the agents, based on the type of interaction between agents - cooperative, competitive, or mixed.
Value Functions in Multiple Agents
-
The Q-values or V-values now involve considering the actions of the other agents and are used to define the optimal policy for each agent given the policies of other agents.
-
To assess and learn a good policy, an individual agent must consider how its own policy affects the cumulative reward, in concert with other agents' policies.
Summary of RL for Optimal Design
- The techniques, methods and strategies used to assess, analyze, and implement optimal outcomes for engineering designs.
- It can solve optimization problems involving multiple objectives and constraints, like minimizing structure volume or maximizing structural strength or stability in a physical system like a truss structure.
Learning Goals in Hierarchical Reinforcement Learning
-
Methods for addressing and overcoming the computational burden of Q-learning, which is a significant concern when dealing with environments featuring many different states, and how to learn a good policy.
-
These methods leverage agents adopting hierarchies and are organized with a hierarchical structure (like feudal rulers/vessals/peasants) and agents or groups taking responsibility for some decision making in different parts of the structural or design space.
-
Methods and strategies are outlined in the presentation, such as state decomposition/division, temporal abstraction methods, option (or sub-task) based strategies
-
The presentation introduces a novel approach to RL for large environments using hierarchical structures to optimize learning strategies.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz explores concepts of conditional probability and optimal path analysis in decision-making scenarios. You will answer questions regarding probability calculations, optimal value functions, and the meaning of optimal paths in various contexts. Test your understanding of these key concepts and their applications.
