Reinforcement Learning¶

Reinforcement Learning Into¶

Imagine teaching a dog tricks.

Over time, the dog learns that sitting when you say “sit” gets a reward, and it dose it more often.

Reinforcement Learning (RL) is just like that - but for computers and algorithms.

It’s a way for machines to learn how to make decisions by trying things out and getting rewards or penalties.

let’s break down RL into its key components using intuitive examples:

RL Concept	Dog Analogy	Financial Analogy (Trading Bot)
Agent	The dog	The trading algorithm
Environment	Your living room	The financial market
Action	Sit, bark, roll	Buy, sell, hold
State	Is the dog standing or sitting?	Stock prices, indicators, portfolio state
Reward	Getting a treat	Profit from a trade or return on investment
Policy	Rule for behavior	Strategy for choosing actions (buy/sell) based on market state

Trial-and-error:

In RL, we model problems using a Markov Decision Process (MDP).

An MDP is a tuple:

\[ MDP = (S,A,P,R,\gamma) \]

Where:

\(S\): Set of states (e.g., stock prices, portfolio)
\(A\): Set of actions (e.g., buy/sell/hold)
\(P(s'|s,a)\): Transition probability from state \(s\) to \(s'\) when taking action \(a\)
\(R(s,a)\): Reward function
\(\gamma \in [0,1]\): Discount factor (how much future rewards are worth today)

The goal: learn a policy \(\pi(a|s)\) that maximizes the expected reward over time.

The Bellman Equation tells how to think about value in TL.

\[ V^{\pi}(s) = \mathbb{E}_{\pi} \left[ R(s,a) + \gamma V^{\pi}(s{\prime}) \right] \]

Tis says:

The value of a state is the reward you get now plus the value of the next state, discounted.

In finance: