Policy Proportional to Exponentiated Reward

A system for ranking text responses first assigns a numerical reward score to each response, and then calculates a 'worth' value for each response using the formula: worth = exp(reward score). Consider two scenarios:

Scenario 1: Response A has a reward score of 3.0, and Response B has a reward score of 1.0. Scenario 2: Response C has a reward score of 8.0, and Response D has a reward score of 6.0.

How does the ratio of worths (Worth_A / Worth_B) in Scenario 1 compare to the ratio of worths (Worth_C / Worth_D) in Scenario 2?

A system for modeling human preferences assigns a numerical reward score, r, to a given text response. This score can be positive, negative, or zero. To use these scores in a specific type of ranking probability model, each score r must be converted into a 'worth' value α that is always positive and strictly increases as r increases. A researcher proposes using the function α = r² + 0.1 for this conversion. Which statement correctly analyzes the suitability of this proposed function?

A system models preferences by first assigning a numerical reward score to a response and then converting it to a 'worth' value using the formula: worth = exp(reward_score). An engineer improves a response, causing its reward score to increase first from 2.0 to 3.0, and then with a further improvement, from 3.0 to 4.0. How does the increase in the response's 'worth' value during the first improvement compare to the increase during the second improvement?