# Questions tagged [dynamic-programming]

For questions related to the dynamic programming paradigm in the context of AI (and, in particular, reinforcement learning).

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### What is the relation between Dynamic Programming and Reinforcement Learning?

Please forgive me for the implicity of the question, as I recently started studying Reinforcement Learning. I am supposed to study a system where the transition probabilities are known and I have to ...
93 views

### Clarification on Formulation of a DP Problem

I am self-teaching reinforcement learning and for now I am trying to solve the following DP problem: A driver is looking for inexpensive parking on the way to his destination. The parking area ...
58 views

### Why solely a one-step-lookahead in value/policy-iteration?

In value iteration and policy iteration we solely consider a one-step-lookahead where the lookahead is from the previous iteraiton and therefore need to sweep over all states and iterate this ...
61 views

### How do we define greedy action for policy improvement for a given stochastic policy?

If we have a deterministic policy $\pi$ with action-value function $q(s,a)$, then a greedy action for policy improvement is defined as $\pi^\prime(s)=\arg\max_{a}q^{\pi}(s,a)$. How do we define a ...
1 vote
35 views

### How is the Markov property of a general state-space model derived?

Below is the derivation for the Markov property of a general state-space model. The red part is not clear. Could someone please explain the steps in the sequential derivation for the red part?
57 views

### Consequence of Dvoretzky Stochastic Approximation Theorem

I am trying to understand all the steps to prove the TD0 algorithm, and I am following a proof which uses a theorem of Tommi Jaakkola, Michael I. Jordan and Satinder P. Singh, in the paper: On the ...
27 views

### How to use UCB or TS in linear programming?

Consider a sequential decision-making problem over $T$ periods where the parameters of the problem should be learned and also optimize an objective function. One possibility is to model the problem as ...
1 vote
270 views

### Interpretation of the Dynamic Time Warping (DTW) graph

How can I interpret ate the DTW graph. I understood the algorithm behind DTW, but I struggle to interpret ate the graph. When I compute the DTW for a signal that is the same signal but shifted in time,...
1 vote
36 views

### Structured policies in dynamic programming: solving a toy example

I am trying to solve a dynamic programming toy example. Here is the prompt: imagine you arrive in a new city for $N$ days and every night need to pick a restaurant to get dinner at. The qualities of ...
1 vote
133 views

### Is there a way use DQN to find the optimal combination of actions (control inputs) and environment parameters?

I am using DQN to find the optimal sequence of control inputs to a dynamic system. The setup is as follows: At the beginning of each episode, the system is initialized to the SAME initial condition ...
33 views

### Usefulness of the state_values calculation in Dynamic Programming

State values are always presented as a central concept in RL, notoriously in the bible, the Sutton&Barton’s book. I have done some exercises trying to improve my understanding, but it is clear ...
1 vote
184 views

### How are these two versions of the Bellman optimality equation related?

I saw two versions of the optimality equation for $V_{*}(s)$ and $Q_{*}(s,a)$. The first one is:  V_{*}(s)=\max _{a} \sum_{s^{\prime}} P_{s s^{\prime}}^{a}\left(r(s, a)+\gamma V_{*}\left(s^{\prime}\...
1 vote
133 views

### Is there a notion of exploration-exploitation tradeoff in dynamic programming (or model-based RL)?

Is there a notion of exploration-exploitation tradeoff in dynamic programming (or model-based RL)?
1 vote
53 views

### How do we get from conditional expectation on both state and action to only state in the proof of the Policy Improvement Theorem?

I'm going through Sutton and Barto's book Reinforcement Learning: An Introduction and I'm trying to understand the proof of the Policy Improvement Theorem, presented at page 78 of the physical book. ...
149 views

### Are policy and value iteration used only in grid world like scenarios?

I am trying to self learn reinforcement learning. At the moment I am focusing on policy and value iteration, and I am finding several problems and doubts. One of the main doubts is given by the fact ...
218 views

### How do we get the value of this state of an MDP, at time-step $h-2$, using dynamic programming?

I am trying to understand the problem below, represented as an MDP with four states (PU, PF, RU, and RF) and two actions (AS). Let's consider V(RF), the value of the state RF. At time-step $h$, V(RF) ...
195 views

### What trait of a planning problem makes reinforcement learning a well suited solution?

Planning problems have been the first problems studied at the dawn of AI (Shakey the robot). Graph search (e.g. A*) and planning (e.g. GraphPlan) algorithms can be very efficient at generating a plan. ...
1 vote
82 views

### Why is the update in-place faster than the out-of-place one in dynamic programming?

In Barto and Sutton's book, it's written that we have two types of updates in dynamic programming Update out-of-place Update in-place The update in-place is the faster one. Why is that the case? ...
164 views

### Is it possible to retrieve the optimal policy from the state value function?

One can easily retrieve the optimal policy from the action value function but how about obtaining it from the state value function?
1 vote
271 views

### Bellman optimality equation in semi Markov decision process

I wrote a Python program for a simple inventory control problem where decision epochs are equally divided (every morning) and there is no lead time for orders (the time between submitting an order ...
430 views

### Why does TD Learning require Markovian domains?

One of my friends and I were discussing the differences between Dynamic Programming, Monte-Carlo, and Temporal Difference (TD) Learning as policy evaluation methods - and we agreed on the fact that ...
1 vote
49 views

### If the transition model is available, why would we use sample-based algorithms?

Sample-based algorithms, like Monte Carlo Algorithms and TD-Learning, are often presented as useful since they do not require a transition model. Assuming I do have access to a transition model, are ...
552 views

### Why is update rule of the value function different in policy evaluation and policy iteration?

In the textbook "Reinforcement Learning: An Introduction", by Richard Sutton and Andrew Barto, the pseudo code for Policy Evaluation is given as follows: The update equation for $V(s)$ comes from the ...
1 vote
420 views

### How does the automated temperature adjustment step work in Soft Actor-Critic?

In section 5 of the paper Soft Actor-Critic Algorithms and Applications, it is proposed an optimization problem to obtain an optimal temperature parameter $\alpha^*_t$. First, one uses the original ...
1k views

### What algorithms are considered reinforcement learning algorithms?

What are the areas/algorithms that belong to reinforcement learning? TD(0), Q-Learning and SARSA are all temporal-difference algorithms, which belong to the reinforcement learning area, but is there ...
204 views

### What are the common techniques one could use to deal with collisions in a transposition table?

Consider an iterative deepening search using a transposition table. Whenever the transposition table is full, what are common strategies applied to replace entries in the table? I'm aware of two ...