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What kind of model would be suitable when I want to consider several things about an attribute?

I'm struggling to figure out what machine learning/deep learning models would be suitable for what I want to achieve

I am trying to create a model which will recommend the optimal item purchases which will give me the highest percentage chance of winning a game. I have enough data (hopefully) to create the model but I want to consider the item purchased and also at what stage in the game was purchased. Can I just add this in as another variable by itself?

Imagine there are 3 items: A, B, and C, and 2 different shops at furthering stages in the game. I want my model to be able to see if the stage of purchase makes a difference for the items. If item A is bought at stage 2 is it still useful at that point in the game, or is it now a weaker choice compared to item B?

However, in my real-life scenario, there will be way more items, shops, and other limitations. I just can't figure out how I can consider items, and stage when some items might be missing entirely from a run of the game.

Originally my plan was to use logistic regression to create my model but now I do not know if it will be able to handle the complexity well enough and if I should attempt to use a deep learning method instead. I have not attempted to create any model yet as I feel I am not understanding how to apply any techniques to my problem.

Here is my understanding of your question -

This is a game with a player who, at every stage has an option of purchasing an item from a specific shop. Depending on the item, shop, and the stage at which it was purchased the user will get a certain reward.

This could be framed as Reinforcement Learning (RL) problem. I believe DQN will work for the above description. RL has the following components - State, Action, Reward, Next State that you need to set up. For your problem, I would design the algorithm in the following way -

State - A tuple consisting of (Stage, Amount the player has earned) Action - [Item A1, Item B1, Item C1, Item A2, Item B2, Item C2] Here the player has to choose an action of purchasing an Item A, B or C from shop 1 or 2. Reward - The reward the player gets for taking a specific action at some stage Next State - A tuple consisting of (Stage + 1, Amount the player has earned)

RL is quite good at learning the rules of a game and getting the optimal score.

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