physics

Multi-agent reinforcement learning

Multi-agent reinforcement learning is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Multi-agent reinforcement learning rather than just read about it. In short: Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment.

Key takeaways

Multi-agent reinforcement learning belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Multi-agent reinforcement learning to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Multi-agent reinforcement learning from memory before moving on to harder problems.

Reference excerpt

Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment. Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex group dynamics. Multi-agent reinforcement learning is closely related to game theory and especially repeated games, as well as multi-agent systems. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation, reciprocity, equity, social influence, language and discrimination.

Definition Similarly to single-agent reinforcement learning, multi-agent reinforcement learning is modeled as some form of a Markov decision process (MDP). Fix a set of agents I = { 1 , . . . , N } {\displaystyle I=\{1,...,N\}} . We then define:

A set S {\displaystyle S} of environment states. One set A i {\displaystyle {\mathcal {A}}_{i}} of actions for each of the agents i ∈ I = { 1 , … , N } {\displaystyle i\in I=\{1,\dots ,N\}} .

P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\vec {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\vec {a}}_{t}={\vec {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\vec {a}}} .

R → a → ( s , s ′ ) {\displaystyle {\vec {R}}_{\vec {a}}(s,s')} is the immediate joint reward after the transition from s {\displaystyle s} to s ′ {\displaystyle s'} with joint action a → {\displaystyle {\vec {a}}} . In settings with perfect information, such as the games of chess and Go, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like self-driving cars, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable stochastic game in the general case, and the decentralized POMDP in the cooperative case.

Cooperation vs. competition When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior:

In pure competition settings, the agents' rewards are exactly opposite to each other, and therefore they are playing against each other. Pure cooperation settings are the other extreme, in which agents get the exact same rewards, and therefore they are playing with each other. Mixed-sum settings cover all the games that combine elements of both cooperation and competition.

Pure competition settings When two agents are playing a zero-sum game, they are in pure competition with each other. Many traditional games such as chess and Go fall under this category, as do two-player variants of video games like StarCraft. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There is no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. The Deep Blue and AlphaGo projects demonstrate how to optimize the performance of agents in pure competition settings. One complexity that is not stripped away in pure competition settings is autocurricula. As the agents' policy is improved using self-play, multiple layers of learning may occur.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Multi-agent reinforcement learning

Start with the simplest possible case. Write down what Multi-agent reinforcement learning claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Multi-agent reinforcement learning before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Multi-agent reinforcement learning ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Multi-agent reinforcement learning

In research: Multi-agent reinforcement learning appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Multi-agent reinforcement learning in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Multi-agent reinforcement learning is common in secondary-school and first-year university syllabi. It links to neighbouring topics Deep learning, Multi-agent systems, Reinforcement learning, so understanding it makes those chapters shorter.
In everyday life: Look for Multi-agent reinforcement learning outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Multi-agent reinforcement learning in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Multi-agent reinforcement learning means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Multi-agent reinforcement learning out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Multi-agent reinforcement learning in simple terms?

Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment.

Why does Multi-agent reinforcement learning matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Multi-agent reinforcement learning?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Multi-agent reinforcement learning.