Final answer:
To find the oscillating steady-state strength values of a classifier receiving a fixed reward every other iteration and placing bids based on its strength, we use a balance equation. The gains from rewards must equal the losses from bids over two iterations, leading us to determine the two strength values and their corresponding bid amounts at equilibrium.
Step-by-step explanation:
To solve the problem, we consider that the classifier's strength oscillates between two values due to the consistent addition of points on every other iteration and the application of a fixed bid coefficient, Chid, without any taxation. Over time, this will lead the classifier to reach a steady-state where the increases due to the points being added will be balanced out across iterations by the bids placed using the Chid coefficient.
Let's denote the two oscillating strength values as S1 and S2, where S1 is the strength before getting the 10-point increase, and S2 is the strength after. Since the classifier earns 10 points on every other iteration, we can say that S2 = S1 + 10. The bid placed on each iteration is then B = Chid × S1 for iterations without the point increase and B = Chid × S2 for iterations with the point increase.
At equilibrium, the amount lost in bids over two iterations, B1 + B2, should equal the 10 points gained, which results in the equation B1 + B2 = Chid × S1 + Chid × S2 = 10. Substituting S2 = S1 + 10 into the preceding equation yields Chid × S1 + Chid × (S1 + 10) = 10. Simplifying gives us 2 × Chid × S1 + Chid × 10 = 10, from which we solve for S1 and by extension, S2.