Before anything else: what is a value function for horizon 2? In short, it’s like a regular old value function but with an extra layer of complexity. Instead of just looking at the immediate reward, this bad boy takes into account the rewards that will be received in the future as well. It’s basically like having a crystal ball and being able to see what’s going to happen next (but without all the ***** side effects).

Now, you might be wondering why anyone would want to use a value function for horizon 2 instead of just sticking with good old fashioned horizon 1. Well, my friend, there are several reasons:

1) It allows us to make better decisions in situations where we need to consider the long-term consequences of our actions. For example, if you’re trying to optimize a manufacturing process and want to minimize waste over time, using a horizon 2 value function can help you identify which actions will result in the least amount of waste overall (rather than just focusing on minimizing waste in the short term).

2) It can be useful for situations where there are multiple stages or phases involved. For example, if we’re trying to optimize a supply chain process that involves several steps and requires us to make decisions at each stage, using a horizon 2 value function can help us identify which actions will result in the best overall outcome (rather than just focusing on maximizing profits at each individual step).

3) It can be useful for situations where there are multiple decision makers involved. For example, if we’re trying to optimize a healthcare system that involves several different stakeholders (such as doctors, patients, and insurance companies), using a horizon 2 value function can help us identify which actions will result in the best overall outcome for all parties involved (rather than just focusing on maximizing profits or minimizing costs).

So, how do we actually calculate this magical horizon 2 value function? Well, it’s not exactly rocket science (although it might feel like it sometimes), but it does involve a bit of math. Here’s the formula:

V(s) = E[R_t + R_{t+1} + … + R_{T-1} | S_t=s]

Where V is the value function for horizon 2, s is the current state, and T is the final time step. The expectation (E) is taken over all possible sequences of rewards that can be received from this point onward.

Now, you might be thinking: “Hey, wait a minute! This formula looks suspiciously similar to the formula for calculating the expected return in finance.” And you’d be right! In fact, there are some interesting parallels between value functions and financial analysis (which is why we sometimes call this field “financial engineering”).

But enough about math real-world applications. One example of a horizon 2 value function in action can be seen in the world of sports betting. Let’s say you’re trying to optimize your betting strategy for a football game that involves multiple stages (such as preseason, regular season, and playoffs). By using a horizon 2 value function, you can identify which bets will result in the best overall outcome over time (rather than just focusing on maximizing profits in the short term).

Another example of a horizon 2 value function in action can be seen in the world of supply chain optimization. Let’s say you’re trying to optimize your inventory management strategy for a manufacturing process that involves multiple stages and requires you to make decisions at each stage (such as ordering raw materials, scheduling production, and shipping finished goods). By using a horizon 2 value function, you can identify which actions will result in the best overall outcome over time (rather than just focusing on minimizing costs or maximizing profits at each individual step).

It’s not exactly rocket science, but it does involve a bit of math and some interesting parallels with financial analysis. But hey, if we can use these techniques to optimize our sports betting strategies or supply chain management processes, who knows what other amazing applications they might have? The possibilities are endless!

Until next time, happy learning (and happy betting)!