Questions tagged [reward-functions]

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

Filter by
Sorted by
Tagged with
12
votes
3answers
662 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 ...
12
votes
4answers
1k 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 ...
8
votes
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 - ...
7
votes
1answer
3k views

Suitable reward function for trading buy and sell orders

I am working to build a deep reinforcement learning agent which can place orders (i.e. limit buy and limit sell orders). The actions are ...
7
votes
2answers
868 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 ...
6
votes
1answer
471 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. ...
5
votes
2answers
415 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, ...
5
votes
1answer
173 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 ...
5
votes
1answer
415 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 ...
5
votes
1answer
159 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 ...
4
votes
2answers
1k 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 ...
4
votes
1answer
1k views

How can I ensure convergence of DDQN, if the true Q-values for different actions in the same state are very close?

I am applying a Double DQN algorithm to a highly stochastic environment where some of the actions in the agent's action space have very similar "true" Q-values (i.e. the expected future ...
4
votes
1answer
369 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 $s_{\text{fixed}}$ ...
4
votes
1answer
462 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 ...
4
votes
0answers
66 views

How define a reward function for a humanoid agent whose goal is to stand up from the ground?

I'm trying to teach a humanoid agent how to stand up after falling. The episode starts with the agent lying on the floor with its back touching the ground, and its goal is to stand up in the shortest ...
4
votes
0answers
53 views

What research has been done on learning non-Markovian reward functions?

Recently, some work has been done planning and learning in Non-Markovian Decision Processes, that is, decision-making with temporally extended rewards. In these settings, a particular reward is ...
3
votes
2answers
94 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 ...
3
votes
2answers
218 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
votes
1answer
162 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 ...
3
votes
1answer
260 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 ...
3
votes
1answer
960 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 ...
3
votes
1answer
529 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?
3
votes
3answers
346 views

Is the policy really invariant under affine transformations of the reward function?

In the context of a Markov decision process, this paper says it is well-known that the optimal policy is invariant to positive affine transformation of the reward function On the other hand, ...
2
votes
1answer
304 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 ...
2
votes
1answer
118 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 ...
2
votes
1answer
86 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(...
2
votes
1answer
67 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
votes
1answer
47 views

Is there a mathematical formalism to deal with a missing reward signal?

Typically, a Reinforcement Learning learning problem is formalized as finding an optimal policy for a Markov Decision Process (MDP). In many real-life situations, however, an agent can only get ...
2
votes
2answers
223 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
votes
1answer
334 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
votes
1answer
69 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
votes
1answer
163 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 ...
2
votes
1answer
96 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
votes
2answers
146 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 ...
2
votes
1answer
55 views

How to encourage the reinforcement-learning agent to reach the goal as quickly as possible, and what's the effect of discount factor?

I am trying to use reinforcement learning to solve a task and compare its performance to humans. The task is to find a single target in a fixed number of locations. At each step, the agent will pick ...
2
votes
1answer
73 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 ...
2
votes
0answers
35 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}(\...
2
votes
0answers
23 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 ...
2
votes
0answers
45 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 ...
2
votes
1answer
115 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 ...
1
vote
1answer
69 views

In addition to the reward function, which other functions do I need to implement Q-learning?

In general, $Q$ function is defined as $$Q : S \times A \rightarrow \mathbb{R}$$ $$Q(s_t,a_t) = Q(s_t,a_t) + \alpha[r_{t+1} + \gamma \max\limits_{a} Q(s_{t+1},a) - Q(s_t,a_t)] $$ $\alpha$ and $\gamma$...
1
vote
1answer
76 views

What happens with policy gradient methods if rewards are differentiable?

I would like some help with understanding why there is no explicit flow of information from the reward gradient to the parameters of the policy in policy gradient methods. What I mean is the following,...
1
vote
1answer
97 views

Which reward function works for recommendation systems using knowledge graphs?

I've been reading this paper on recommendation systems using reinforcement learning (RL) and knowledge graphs (KGs). To give some background, the graph has several (finitely many) entities, of which ...
1
vote
1answer
1k 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. ...
1
vote
1answer
36 views

How do I compute the value function when the reward is only at the end in the context of actor-critic algorithms?

Consider the actor-critic reinforcement learning setting (actor and critic parameterized by a neural network). The reward is given only at the end of the episode (or when there is a timeout there is ...
1
vote
1answer
51 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
1answer
54 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 ...
1
vote
1answer
145 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 ...
1
vote
0answers
50 views

How can we formulate a state-space search problem as a Markov decision process?

A Markov Decision Process (MDP) is a mathematical model for sequential decision-making in stochastic environments. Formally, we can define an MDP as a tuple $M = (S, A, p, \gamma)$, where $S$ is the ...
1
vote
0answers
32 views

How to teach Machine Learning Agent to destroy replicating objects in a puzzle game?

I have an unusual but very interesting problem. I have a game that is very similar to Toon Blast (a puzzle mobile game). It's based on a Match-2 mechanic in which you can destroy 2 or more connected ...