Questions tagged [reward-functions]

For questions about rewards functions (e.g. in the context of reinforcement learning, which may be denoted as $R(s, a)$).

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2
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1answer
48 views

Intuition behind $1-\gamma$ and $\frac{1}{1-\gamma}$ for calculating discounted future state distribution and discounted reward

In the appendix of the Constrained Policy Optimization (CPO) paper (Arxiv), the authors denote the discounted future state distribution $d^\pi$ as: $$d^\pi(s) = (1-\gamma) \sum_{t=0}^\infty{\gamma^t P(...
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1answer
101 views

How to improve the reward signal when the rewards are sparse?

In cases where the reward is delayed, this can negatively impact a models ability to do proper credit assignment. In the case of a sparse reward, are there ways in which this can be negated? In a ...
2
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1answer
51 views

Can the rewards be matrices when using DQN?

I have a basic question. I'm working towards developing a reward function for my DQN. I'd like to train an RL agent to edit pixels on an image. I understand that convolutions are ideal for working ...
2
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1answer
63 views

How can I go from $R(s)$ to $R(s,a)$ in this specific MDP?

I'm trying to implement a research paper, as explained in this other post, here the author of the paper assumed R as a function of both states and actions, while the code (and the MDP) I'm using to ...
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1answer
139 views

What is the difference between a fitness function and a reward function?

In reinforcement learning (RL), the reward function (RF), which can be denoted as $r(s)$, $r(s, a)$, $r(s, a, s')$, $r(s, s')$ depending on its specific definition, provides the learning signal, which ...
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0answers
26 views

Is better to reward short- or long-term progress in Q-learning?

I have been training some kind of agent to reach a target using a Q-learning based approach, and I have tried two different types of rewards: Long-term reward: $\mathrm{reward} = - \mathrm{distance}(\...
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0answers
51 views

Is my reward function non-Markovian?

I am working on an RL problem where the time when the agent obtains the reward for taking action $a$ in time step $t$ is stochastic. In fact, there is no immediate reward for taking action $a$ in time ...
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1answer
51 views

If the reward function of an environment depends on some initial conditions, should I create a separate environment for each condition?

I would like some guidance on how to design an Environment for a Reinforcement Learning agent where the stopping conditions and rewards for the environment change based on an initial set of input ...
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0answers
36 views

Thompson sampling with Bernoulli prior and non-binary reward update

I am solving a problem for which I have to select the best possible servers (level 1) to hit for a given data. These servers (level 1) in turn hit some other servers (level 2) to complete the request. ...
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0answers
22 views

How can I discourage the RL agent from drawing in a zero-sum game?

My agent receives $1, 0, -1$ rewards for winning, drawing, and losing the game, respectively. What would be the consequences of setting reward to $-1$ for draws? Would that encourage the agent to win ...
6
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1answer
166 views

Why does a negative reward for every step really encourage the agent to reach the goal as quickly as possible?

If we shift the rewards by any constant (which is a type of reward shaping), the optimal state-action value function (and so optimal policy) does not change. The proof of this fact can be found here. ...
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1answer
111 views

What is the optimal value function of the shifted version of the reward function?

Similarly to this question that I asked some time ago, what is the optimal value function of the shifted (by some constant $c$) version of some reward function? More precisely, let's assume that $r(s, ...
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2answers
140 views

How should I define the reward function to solve the Wumpus game with deep Q-learning?

I'm writing a DQN agent for the Wumpus game. Is the reward function to train the Q-networks (target network and policy) the same as the score of the game, i.e. +1000 for picking up gold, -1000 for ...
2
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1answer
95 views

What are proxy reward functions?

The understanding I have is that they somehow adjust the objective to make it easier to meet, without changing the reward function. ... the observed proxy reward function is the approximate solution ...
3
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2answers
104 views

How to apply Q-learning when rewards is only available at the last state?

I have a scheduling problem in which there are $n$ slots and $m$ clients. I am trying to solve the problem using Q-learning so I have made the following state-action model. A state $s_t$ is given by ...
3
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1answer
408 views

What are the pros and cons of sparse and dense rewards in reinforcement learning?

From what I understand, if the rewards are sparse the agent will have to explore more to get rewards and learn the optimal policy, whereas if the rewards are dense in time, the agent is quickly guided ...
2
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0answers
35 views

How to combine two differently equally important signals into the reward function, that have different scales?

I have two signals that I want to use to model my reward. The first one is the CPU TIME: running mean from this diagram: The second one is the MAX RESIDUAL from this diagram: Since they are both ...
9
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3answers
346 views

Why is the reward in reinforcement learning always a scalar?

I'm reading Reinforcement Learning by Sutton & Barto, and in section 3.2 they state that the reward in a Markov decision process is always a scalar real number. At the same time, I've heard about ...
4
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2answers
268 views

What are some best practices when trying to design a reward function?

Generally speaking, is there a best-practice procedure to follow when trying to define a reward function for a reinforcement-learning agent? What common pitfalls are there when defining the reward ...
2
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1answer
218 views

Is a reward given at every step or only given when the RL agent fails or succeeds?

In reinforcement learning, an agent can receive a positive reward for correct actions and a negative reward for wrong actions, but does the agent also receive rewards for every other step/action?
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2answers
89 views

Can rewards be decomposed into components?

I'm training a robot to walk to a specific $(x, y)$ point using TD3, and, for simplicity, I have something like ...
4
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1answer
194 views

Why does shifting all the rewards have a different impact on the performance of the agent?

I am new to reinforcement learning. For my application, I have found out that if my reward function contains some negative and positive values, my model does not give the optimal solution, but the ...
5
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1answer
226 views

How do I convert an MDP with the reward function in the form $R(s,a,s')$ to and an MDP with a reward function in the form $R(s,a)$?

The AIMA book has an exercise about showing that an MDP with rewards of the form $r(s, a, s')$ can be converted to an MDP with rewards $r(s, a)$, and to an MDP with rewards $r(s)$ with equivalent ...
4
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1answer
70 views

How should I handle invalid actions in a grid world?

I'm building a really simple experiment, where I let an agent move from the bottom-left corner to the upper-right corner of a $3 \times 3$ grid world. I plan to use DQN to do this. I'm having trouble ...
3
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1answer
75 views

Why is the reward function $\text{reward} = 1/{(\text{cost}+1)^2}$ better than $\text{reward} =1/(\text{cost}+1)$?

I have implemented a simple Q-learning algorithm to minimize a cost function by setting the reward to the inverse of the cost of the action taken by the agent. The algorithm converges nicely, but ...
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1answer
65 views

What is the relationship between the reward function and the value function?

To clarify it in my head, the value function calculates how 'good' it is to be in a certain state by summing all future (discounted) rewards, while the reward function is what the value function uses ...
2
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1answer
82 views

How can I implement the reward function for an 8-DOF robot arm with TRPO?

I need to get an 8-DOF (degrees of freedom) robot arm to move a specified point. I need to implement the TRPO RL code using OpenAI gym. I already have the gazebo environment. But I am unsure of how to ...
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4answers
720 views

Counterexamples to the reward hypothesis

On Sutton and Barto's RL book, the reward hypothesis is stated as that all of what we mean by goals and purposes can be well thought of as the maximization of the expected value of the cumulative ...
2
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1answer
80 views

What is the difference between success rate and reward when dealing with binary and sparse rewards?

In OpenAI Gym "reward" is defined as: reward (float): amount of reward achieved by the previous action. The scale varies between environments, but the ...
2
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1answer
279 views

What is the optimal value function of the scaled version of the reward function?

Consider the reward function $r(s, a)$ with optimal state-action value function $q_*(s, a)$. What would be the optimal state-action value function of $c r(s, a)$, for $c \in \mathbb{R}$? Would it be $...
2
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1answer
133 views

How does the initialization of the value function and definition of the reward function affect the performance of the RL agent?

Is there any empirical/theoretical evidence on the effect of initial values of state-action and state values on the training of an RL agent (the values an RL agent assigns to visited states) via MC ...
6
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2answers
542 views

How do we define the reward function for an environment?

How do you actually decide what reward value to give for each action in a given state for an environment? Is this purely experimental and down to the programmer of the environment? So, is it a ...
1
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1answer
738 views

What is the reward system of reinforcement learning?

Can you describe this reward system in more detail? I understand that the environment sends a signal indicating whether or not the action taken by the agent was 'good' or not, but it seems too simple. ...
4
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1answer
300 views

Can the rewards be stochastic when the transition model is deterministic?

Suppose we have a deterministic environment where knowing $s,a$ determines $s'$. Is it possible to get two different rewards $r\neq r'$ in some state $s_{\text{fixed}}$? Assume that $s_{\text{fixed}}$ ...
5
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2answers
224 views

How are the reward functions $R(s)$, $R(s, a)$ and $R(s, a, s')$ equivalent?

In this video, the lecturer states that $R(s)$, $R(s, a)$ and $R(s, a, s')$ are equivalent representations of the reward function. Intuitively, this is the case, according to the same lecturer, ...
2
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1answer
53 views

Why does potential-based reward shaping seem to alter the optimal policy in this case?

It is known that every potential function won't alter the optimal policy [1]. I lack of understanding why is that. The definition: $$R' = R + F,$$ with $$F = \gamma\Phi(s') - \Phi(s),$$ where, let's ...
2
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2answers
129 views

How to define a reward function in POMDPs?

How do I define a reward function for my POMDP model? In the literature, it is common to use one simple number as a reward, but I am not sure if this is really how you define a function. Because this ...
3
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1answer
113 views

Why is the equation $r(s', a, s') =\sum_{r \in \mathcal{R}} r \frac{p\left(s^{\prime}, r \mid s, a\right)}{p\left(s^{\prime} \mid s, a\right)}$true?

I am referring to eq. 3.6 (page 49) based on Sutton's online book and can be found in an image below. I could not make sense of the final derivation of the equation $r(s, a, s')$. My question is ...
8
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1answer
2k views

What are other ways of handling invalid actions in scenarios where all rewards are either 0 (best reward) or negative?

I created an OpenAI Gym environment, and I would like to check the performance of the agent from OpenAI Baselines DQN approach on it. In my environment, the best possible outcome for the agent is 0 - ...