How does reinforcement learning let AI learn by trial and error - like a child touching a hot stove?

No instructions, no examples - just rewards, punishments, and a lot of practice.

The answer

Reinforcement learning (RL) is a paradigm where an agent learns to make decisions by interacting with an environment and receiving reward or penalty signals, without being explicitly told the correct actions. The mathematical framework, built on Markov Decision Processes, was formalized by Richard Sutton and Andrew Barto in their influential 1998 textbook, now cited over 50,000 times. RL maps closely to how animals learn through conditioning and has powered many of AI's most impressive achievements, from playing games at superhuman levels to controlling robots and optimizing data center cooling at Google.

Source: MIT Press - Reinforcement Learning: An Introduction

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