Consider the situation on sports trading. Suppose I take a back bet on team A, at price 1.8 with stake \$10, this would result a potential profit of \$8 or a potential loss \$10. Then I take a lay bet on team A, at price 1.5 with stake \$15, this bet would result a profit \$15 or loss \$7.5
Combining these two bets, we will have a profit \$0.5 (if team A wins) or \$5 (if team A loses).
So my two objectives here are to maximise these two profits coming from two scenarios (even though we will only get one of these, but as long as both of them are greater than 0, we are happy to choose either one).
Would Multi-Objective Reinforcement Learning be overkill to this problem? One of the reasons why I want to solve this in Multi-Objective instead of single-objective(maximise total profit) is that I find it difficult to write down the reward at each state. In Multi-Objective, the rewards in both situation are clear, but in single-objective, we don't actually know the exact reward, we have the uncertainly in this case. We only know how much we will get after the match ends. Is there any way to solve this in single-objective approach?
I have also looked up some articles about Multi-Objective Reinforcement Learning, one approach is to take the weighted average of these two profit. However, this seems to be equivalent to assuming the probability of teamA winning. How to overcome this problem if I happen to use Multi-Objective Reinforcement Learning?