Paper recasts evolution-strategy updates as center-of-mass shifts
Original title: Center-of-Mass Interpretation of Evolution Strategies
The mean-subtracted update matches a reward-weighted displacement for any finite population when rewards are nonnegative.
The paper replaces the usual smoothed-gradient view of evolution strategies with a geometric one. Each perturbed model is a particle and its reward is mass; after scoring, the population balances at a reward-weighted center of mass. The authors show the mean-subtracted update is exactly that displacement, scaled by a factor that depends on mean reward, for any finite population. Nonnegative rewards can be arranged by adding a constant. With a large population or antithetic sampling, the model moves from its current point toward that center of mass.
- Subtracting mean reward changes where the displacement is measured from.
- Adding a constant to every reward leaves the update unchanged.
- The identity is claimed exact for any finite population.
- Antithetic sampling places the centroid on the current model.
From the original article
1 min read at arxiv.orgEvolution strategies (ES) update a model by sampling a population of perturbed copies, scoring each one, and moving in the reward-weighted direction of the perturbations. This update is usually presented as an estimate of a smoothed gradient. We present a geometrical interpretation of this update instead.
By Akshat Gupta · arxiv.org
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