How to generalise over multiple dependent actions in Reinforcement Learning - reinforcement-learning

Question

I am trying to build an RL agent to price paid for airline seats (not the ticket). The general set up is:
After choosing their flights (for n people on a booking), a customer will view a web page with the available seat types and their prices visible.
They select between zero and n seats from a seat map with a variety of different prices for different seats, to be added to their booking.
After perhaps some other steps, they pay for the booking and the agent is rewarded with the seat revenue.
I have not decided on a general architecture yet. I want to take various booking and flight information into account, so I know I will be using function approximation (most likely a neural net) to generalise over the state space.
However, I am less clear on how to set up my action space. I imagine an action would amount to a vector with a price for each different seat type. If I have, for example, 8 different seat types, and 10 different price points for each, this gives me a total of 10^8 different actions, many of which will be very similar. Additionally, each sub-action (pricing one seat type) is somewhat dependent on the others, in the sense that the price of one seat type will likely affect the demand (and hence reward contribution) for another. Hence, I doubt the problem can be decomposed into a set of sub-problems.
I'm interested if there has been any research into dealing with a problem like this. Clearly any agent I build needs some way to generalise across actions to some degree, since collecting real data on millions of actions is not possible, even just for one state.
As I see it, this comes down to two questions:
Is it possible to get an agent to understand actions in relative terms? Say for example, one set of potential prices is [10, 12, 20]. Can I get my agent to realise that there is a natural ordering there, and that the first two pricing actions are more similar to each other than to the third possible action?
Further to this, is it possible to generalise from this set of actions - could an agent be set up to understand that the set of prices [10, 13, 20] is very similar to the first set?
I haven't been able to find any literature on this, especially relating to the second question - any help would be much appreciated!

Answer 1

Correct me if I'm wrong, but I am going to assume this is what you are asking and will answer accordingly.
I am building an RL and it needs to be smart enough to understand that if I were to buy one airplane ticket, it will subsequently affect the price of other airplane tickets because there is now less supply.
Also, the RL agent must realize that actions very close to each other are relatively similar actions, such as [10, 12, 20] ≈ [10, 13, 20]
1) In order to provide memory to your RL agent, you can do this in two ways. The easy way is to feed the states as a vector of past purchased tickets, as well as the current ticket.
Example: Let's say we build the RL to remember at least the past 3 transactions. At the very beginning, our state vector will be [0, 0, 3], meaning that there was no purchases of tickets previously (the zeros), and currently, we are purchasing ticket #3. Then, the next time step's state vector can be [0, 3, 6], telling the RL agent that previously, ticket #3 has been picked, and now we're buying ticket #6. The neural network will learn that the state vector [0, 0, 6] should map to a different outcome compared to [0, 3, 6], because in the first case, ticket #6 was the first ticket purchased and there was lots of supply. But in the 2nd case, ticket 3 was already sold, so now all the remaining tickets went up in price.
The proper and more complex way would be to use a recurrent neural network as your function approximator for your RL agent. The recurrent neural network architecture allows for certain "important" states to be remembered by the neural network. In your case, the amount of tickets purchased previously is important, so the neural network will remember the previously purchased tickets, and calculate the output accordingly.
2) Any function approximation reinforcement learning algorithm will automatically generalize sets of actions close to each other. The only RL architectures that would not do this would be tabular based approaches.
The reason is the following:
We can think of these function approximators simply as a line. Neural networks simply build a highly nonlinear continuous line (neural networks are trained using backpropagation and gradient descent, so they must be continuous), and a set of states will map to a unique set of outputs. Because it is a line, sets of states that are very similar SHOULD map to outputs that are also very close. In the most basic case, imagine y = 2x. If our input x = 1, our y = 2. And if our input x is 1.1, which is very close to 1, our output y = 2.2, which is very close to 2 because they are on a continuous line.
For tabular approach, there is simply a matrix. On the y axis, you have the states, and on the x axis, you have the actions. In this approach, the states and actions are discrete. Depending on the discretization, the difference can be massive, and if the system is poorly discretized, the actions very close to each other MAY not be generalized.
I hope this helps, please let me know if anything is unclear.