Questions tagged [rewards]

For questions related to the concept of reward, for example, in the context of reinforcement learning and Markov decision processes. For questions related to reward functions, reward design, reward shaping, reward hacking, etc., there are also those specific tags, so you use them instead of this generic one, unless your question is also about the concept of reward.

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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 ...
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  • 223
12 votes
6 answers
2k views

What would motivate a machine?

Currently, within the AI development field, the main focus seems to be on pattern recognition and machine learning. Learning is about adjusting internal variables based on a feedback loop. Maslow's ...
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10 votes
1 answer
3k views

What is the difference between expected return and value function?

I've seen numerous mathematical explanations of reward, value functions $V(s)$, and return functions. The reward provides an immediate return for being in a specific state. The better the reward, the ...
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9 votes
2 answers
10k views

How do I handle negative rewards in policy gradients with the cross-entropy loss function?

I am using policy gradients in my reinforcement learning algorithm, and occasionally my environment provides a severe penalty (i.e. negative reward) when a wrong move is made. I'm using a neural ...
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  • 199
7 votes
1 answer
3k views

Why does the "reward to go" trick in policy gradient methods work?

In the policy gradient method, there's a trick to reduce the variance of policy gradient. We use causality, and remove part of the sum over rewards so that only actions happened after the reward are ...
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6 votes
1 answer
196 views

Why cannot an AI agent adjust the reward function directly?

In standard Reinforcement Learning the reward function is specified by an AI designer and is external to the AI agent. The agent attempts to find a behaviour that collects higher cumulative discounted ...
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  • 61
6 votes
1 answer
78 views

Reward interpolation between MDPs. Will an optimal policy on both ends stay optimal inside the interval?

Say I've got two Markov Decision Processes (MDPs): $$\mathcal{M_0} = (\mathcal{S}, \mathcal{A}, P, R_0),\quad\text{and}\quad\mathcal{M}_1 = (\mathcal{S}, \mathcal{A}, P, R_1)$$ Both have the same set ...
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  • 1,833
5 votes
2 answers
2k views

Reinforcement Learning with long term rewards and fixed states and actions

I have read a lot about RL algorithms, that update the action-value function at each step with the currently gained reward. The requirement here is, that the reward is obtained after each step. I ...
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  • 329
5 votes
2 answers
1k views

Is there any difference between reward and return in reinforcement learning?

I am reading Sutton and Barto's book on reinforcement learning. I thought that reward and return were the same things. However, in Section 5.6 of the book, 3rd line, first paragraph, it is written: ...
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  • 331
5 votes
1 answer
585 views

If the current state is $S_t$ and the actions are chosen according to $\pi$, what is the expectation of $R_{t+1}$ in terms of $\pi$ and $p$?

I'm trying to solve exercise 3.11 from the book Sutton and Barto's book (2nd edition) Exercise 3.11 If the current state is $S_t$ , and actions are selected according to a stochastic policy $\pi$, ...
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  • 362
5 votes
1 answer
726 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 ...
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4 votes
3 answers
695 views

Is there an upper limit to the maximum cumulative reward in a deep reinforcement learning problem?

Is there an upper limit to the maximum cumulative reward in a deep reinforcement learning problem? For example, you want to train a DQN agent in an environment, and you want to know what the highest ...
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4 votes
2 answers
575 views

Is there a good ratio between the positive and negative rewards in reinforcement learning?

Is there an ideal ratio in reinforcement learning between the positive and negative rewards? Suppose I have the scenario of moving a robot across the river. There are two options, walk across the ...
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4 votes
2 answers
303 views

Why is regret so defined in MABs?

Consider a multi-armed bandit(MAB). There are $k$ arms, with reward distributions $R_i$ where $1 \leq i \leq k$. Let $\mu_i$ denote the mean of the $i^{th}$ distribution. If we run the multi-armed ...
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4 votes
1 answer
938 views

Non-differentiable reward function to update a neural network

In Reinforcement Learning, when reward function is not differentiable, a policy gradient algorithm is used to update the weights of a network. In the paper Neural Architecture Search with ...
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4 votes
1 answer
356 views

How to evaluate an RL algorithm when used in a game?

I'm planning to create a web-based RL board game, and I wondered how I would evaluate the performance of the RL agent. How would I be able to say, "Version X performed better than version Y, as ...
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4 votes
1 answer
44 views

$E_{\pi}[R_{t+1}|S_t=s,A_t=a] = E[R_{t+1}|S_t=s,A_t=a]$?

I would like to solve the first question of Exercise 3.19 from Sutton and Barto: Exercise 3.19 The value of an action, $q_{\pi}(s, a)$, depends on the expected next reward and the expected sum of the ...
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  • 157
4 votes
2 answers
142 views

How can we prevent AGI from doing drugs?

I recently read some introductions to AI alignment, AIXI and decision theory things. As far as I understood, one of the main problems in AI alignment is how to define a utility function well, not ...
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4 votes
1 answer
235 views

Immediate reward received in Atari game using DQN

I am trying to understand the different reward functions modelled in a reinforcement learning problem. I want to be able to know how the temporal credit assignment problem, (where the reward is ...
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  • 1,221
4 votes
1 answer
273 views

How to assign rewards in a non-Markovian environment?

I am quite new to the Reinforcement Learning domain and I am curious about something. It seems to be the case that the majority of current research assumes Markovian environments, that is, future ...
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4 votes
1 answer
311 views

Can someone please help me validate my MDP?

Problem Statement : I have a system with four states - S1 through S4 where S1 is the beginning state and S4 is the end/terminal state. The next state is always better than the previous state i.e if ...
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  • 83
4 votes
1 answer
217 views

What could be the cause of the drop in the reward in A3C?

The mean episodic reward is generally increasing, but it has spontaneous drops, and I'm not sure of their cause. The problem has a sparse reward, batch size=2000, <...
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  • 163
3 votes
2 answers
881 views

What is the difference between a loss function and reward/penalty in Deep Reinforcement Learning?

In Deep Reinforcement Learning (DRL) I am having difficulties in understanding the difference between a Loss function, a reward/penalty and the integration of both in DRL. Loss function: Given an ...
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  • 131
3 votes
1 answer
101 views

How do we derive the expression for average reward setting in continuing tasks?

In the average reward setting we have: $$r(\pi)\doteq \lim_{h\rightarrow\infty}\frac{1}{h}\sum_{t=1}^{h}\mathbb{E}[R_{t}|S_0,A_{0:t-1}\sim\pi]$$ $$r(\pi)\doteq \lim_{t\rightarrow\infty}\mathbb{E}[R_{t}...
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3 votes
1 answer
361 views

How is the reward in reinforcement learning different from the label in supervised learning problems?

How is the notion of immediate reward used in the reinforcement learning different from the notion of a label we find in the supervised learning problems?
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  • 35
3 votes
1 answer
283 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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  • 77
3 votes
1 answer
55 views

Do all expert trajectories have the same starting state in apprenticeship learning?

In the apprenticeship learning algorithm described by Ng et al. in Apprenticeship Learning via Inverse Reinforcement Learning, they mention that expert trajectories come in the form of $\{s_0^i, s_1^i\...
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  • 1,221
3 votes
1 answer
160 views

Are there any reliable ways of modifying the reward function to make the rewards less sparse?

If I am training an agent to try and navigate a maze as fast as possible, a simple reward would be something like \begin{align} R(\text{terminal}) &= N - \text{time}\ \ , \ \ N \gg \text{...
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  • 133
3 votes
1 answer
81 views

Is my interpretation of the return correct?

Sutton and Barto 2018 define the discounted return $G_t$ the following way (p 55): Is my interpretation correct? Or should all "1" be in the same column?
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3 votes
1 answer
415 views

How should I design the reward function for racing game (where the goal is to reach finishing line before the opponent)?

I'm building an agent for a racing game. In this game, there is a randomized map where there are speed boosts for the player to pick up and obstacles that act to slow the player down. The goal of the ...
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3 votes
1 answer
421 views

Appropriate algorithm for RL problem with sparse rewards, continuous actions and significant stochasticity

I'm working on a RL problem with the following properties: The rewards are extremely sparse i.e. all rewards are 0 except the terminal non-zero reward. Ideally I would not use any reward engineering ...
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  • 129
3 votes
1 answer
77 views

Can I have different rewards for a single action based on which state it transitions to?

I am working on an MDP where there are four states and ten actions. I am supposed to derive the optimal policy to reach the desired state. At any state, a particular action can take you to any of the ...
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  • 83
3 votes
1 answer
119 views

How do I represent sample efficiency of RL rewards in mathematical notation?

I define sample efficiency as the area under the curve/graph, where $x$-axis is the number of episodes while y-axis is the cumulative reward for that episode. I would like to formally define it with a ...
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3 votes
1 answer
139 views

How can I fix jerky movement in a continuous action space

I am training an agent to do object avoidance. The agent has control over its steering angle and its speed. The steering angle and speed are normalized in a $[−1,1]$ range, where the sign encodes ...
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3 votes
1 answer
47 views

Shouldn't expected return be calculated for some faraway time in the future $t+n$ instead of current time $t$?

I am learning RL for the first time. It may be naive, but it is a bit odd to grasp this idea that, if the goal of RL is to maximize the expected return, then shouldn't the expected return be ...
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  • 331
3 votes
1 answer
155 views

Can recovering a reward function using IRL lead to better policies compared to reward shaping?

I am working on a research project about the different reward functions being used in the RL domain. I have read up on Inverse Reinforcement Learning (IRL) and Reward Shaping (RS). I would like to ...
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  • 1,221
3 votes
1 answer
283 views

Given specific rewards, how can I calculate the returns for each time step?

Let's use Excercise 3.8 from Sutton, Barto - Introduction to RL: Suppose $\gamma = 0.5$ and following sequence of rewards is received $R_1=-1$ , $R_2=2$ , $R_3=6$ , $R_4=3$ , $R_5=2$ , with $T=5$ ...
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3 votes
0 answers
115 views

How does normalization of the inputs work in the context of PPO?

What does the normalization of the inputs mean in the context of PPO? At each time step of an episode, I only know the values of this time step and of the previous ones, if I take track of them. This ...
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  • 161
3 votes
0 answers
111 views

What are the guidelines for defining a reward function in reinforcement learning (bandit problem)?

I'm working currently on a problem and I'm using RL (bandit problem). In my system, I have an agent that chooses an action among $k$ possible actions, and a user that decides whether the agent ...
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  • 31
3 votes
1 answer
229 views

How to avoid rapid actuator movements in favor of smooth movements in a continuous space and action space problem?

I'm working on a continuous state / continuous action controller. It shall control a certain roll angle of an aircraft by issuing the correct aileron commands (in $[-1, 1]$). To this end, I use a ...
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  • 151
2 votes
1 answer
773 views

Should RL rewards diminish over time?

Should a reward be cumulative or diminish over time? For example, say an agent performed a good action at time $t$ and received a positive reward $R$. If reward is cumulative, $R$ is carried on ...
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2 votes
2 answers
331 views

Simulating successful trajectories in Montezuma's Revenge turns out to be unsuccessful

I have written code in OpenAI's gym to simulate a random playing in Montezuma's Revenge where the agent randomly samples actions from the action space and tries to play the game. A success for me is ...
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2 votes
1 answer
287 views

How to deal with small reward values

In my environment rewards are generally small, e.g. [-0.01, 0.01]. My concern is that small reward values might get dominated or distorted by the noise during the training. Does it make sense to scale ...
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  • 197
2 votes
1 answer
539 views

Why do my rewards reduce after extensive training using D3QN?

I am running a drone simulator for collision avoidance using a slight variant of D3QN. The training is usually costly (runs for at least a week) and I have observed that reward function gradually ...
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2 votes
1 answer
97 views

How should I take into consideration the number of steps in the reward function?

I am currently implementing the paper Active Object Localization with Deep Reinforcement Learning in Python. While reading about the reward scheme I came across the following: Finally, the proposed ...
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  • 293
2 votes
1 answer
154 views

Why is training longer not better in reinforcement learning?

I have trained an RL agent (PPO) for 6 million steps to solve the OpenAI gym LunarLander-v2. Surprisingly, the agent performs best already after 320K steps and is getting worse after that. In the ...
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  • 213
2 votes
1 answer
1k views

Why is the expected return in Reinforcement Learning (RL) computed as a sum of cumulative rewards?

Why is the expected return in Reinforcement Learning (RL) computed as a sum of cumulative rewards? Would it not make more sense to compute $\mathbb{E}(R \mid s, a)$ (the expected return for taking ...
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2 votes
1 answer
318 views

How do we know that the algorithm has converged and ensures the highest possible reward?

I started learning about Q table from this blog post Introduction to reinforcement learning and OpenAI Gym, by Justin Francis, which has a line as below - After so many episodes, the algorithm will ...
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2 votes
2 answers
244 views

Can Reinforcement Learning solve problems, where certain elements in the environement are randomly located?

I want to solve a problem using Reinforcement Learning on a 20x20 board. An agent (a mouse) has to get the highest possible rewards as fast as possible by collecting cheese, which there are 10 in ...
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2 votes
1 answer
59 views

How do I avoid an agent to tend to terminate in a negative state when time needs to be taken into account?

In an unknown environment, how do I avoid an agent to tend to terminate its trajectory in a negative state when time needs to be taken into account? Suppose the following example to make my question ...
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