Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL), these problems are addressed by (i)~designing a reward function that simultaneously describes all requirements or (ii)~combining modular value functions that encode them individually. Though effective, these methods have critical downsides. Designing good reward functions that balance different objectives is challenging, especially as the number of objectives grows. Moreover, implicit interference between goals may lead to performance plateaus as they compete for resources, particularly when training on-policy. Similarly, selecting parameters to combine value functions is at least as hard as designing an all-encompassing reward, given that the effect of their values on the overall policy is not straightforward.

The paper studies a form of constrained reinforcement learning in which the constraints are bounds on the value functions for auxiliary rewards. This allows a more expressive formulation than the common approach of defining the reward as a linear combination of multiple objectives. The authors show that under certain conditions, the constraint optimization problem has zero duality gap, implying that a solution can be found by solving the dual optimization problem, which is convex. The authors also extend this analysis to the case for which the policy is parameterized. Theorem 1 assumes that Slater's condition holds, which is problematic for two reasons. Slater's condition is usually defined for convex constraints, but the authors specifically state that the constraints in PI are non-convex.

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Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning (RL), these problems are addressed by (i) designing a reward function that simultaneously describes all requirements or (ii) combining modular value functions that encode them individually. Though effective, these methods have critical downsides. Designing good reward functions that balance different objectives is challenging, especially as the number of objectives grows. Moreover, implicit interference between goals may lead to performance plateaus as they compete for resources, particularly when training on-policy. Similarly, selecting parameters to combine value functions is at least as hard as designing an all-encompassing reward, given that the effect of their values on the overall policy is not straightforward.

Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning (RL), these problems are addressed by (i) designing a reward function that simultaneously describes all requirements or (ii) combining modular value functions that encode them individually. Though effective, these methods have critical downsides. Designing good reward functions that balance different objectives is challenging, especially as the number of objectives grows. Moreover, implicit interference between goals may lead to performance plateaus as they compete for resources, particularly when training on-policy.