This is the third of five posts in the Risks from Learned Optimization Sequence based on the paper “Risks from Learned Optimization in Advanced Machine Learning Systems” by Evan Hubinger, Chris van Merwijk, Vladimir Mikulik, Joar Skalse, and Scott Garrabrant. Each post in the sequence corresponds to a different section of the paper.

In this post, we outline reasons to think that a mesa-optimizer may not optimize the same objective function as its base optimizer. Machine learning practitioners have direct control over the base objective function—either by specifying the loss function directly or training a model for it—but cannot directly specify the mesa-objective developed by a mesa-optimizer. We refer to this problem of aligning mesa-optimizers with the base objective as the inner alignment problem. This is distinct from the outer alignment problem, which is the traditional problem of ensuring that the base objective captures the intended goal of the programmers.

Current machine learning methods select learned algorithms by empirically evaluating their performance on a set of training data according to the base objective function. Thus, ML base optimizers select mesa-optimizers according to the output they produce rather than directly selecting for a particular mesa-objective. Moreover, the selected mesa-optimizer's policy only has to perform well (as scored by the base objective) on the training data. If we adopt the assumption that the mesa-optimizer computes an optimal policy given its objective function, then we can summarize the relationship between the base and mesa- objectives as follows:(17) $\begin{matrix} θ^{*} & = {argmax}_{θ} E (O_{base} (π_{θ})), where π_{θ} & = {argmax}_{π} E (O_{mesa} (π | θ)) \end{matrix}$ That is, the base optimizer maximizes its objective $O_{base}$ by choosing a mesa-optimizer with parameterization $θ$ based on the mesa-optimizer's policy $π_{θ}$ , but not based on the objective function $O_{mesa}$ that the mesa-optimizer uses to compute this policy. Depending on the base optimizer, we will think of $O_{base}$ as the negative of the loss, the future discounted reward, or simply some fitness function by which learned algorithms are being selected.

An interesting approach to analyzing this connection is presented in Ibarz et al, where empirical samples of the true reward and a learned reward on the same trajectories are used to create a scatter-plot visualization of the alignment between the two.

...

Posts

Comments