---
title: 'ME-MAP-Elites: Multi-Emitter Search'
url: https://www.emergentmind.com/topics/multi-emitter-map-elites-me-map-elites
type: topic
---

# ME-MAP-Elites: Multi-Emitter Search

Multi-Emitter MAP-Elites (ME-MAP-Elites) denotes a class of quality-diversity (QD) algorithms that enhance the classical MAP-Elites framework by deploying multiple, potentially heterogeneous, emitters to accelerate and diversify exploration and exploitation in high-dimensional search spaces. This approach has yielded state-of-the-art empirical results in generating archives of high-performing and diverse solutions across both standard optimization and complex robotics tasks [2007.05352, 2303.06137].

## 1. Quality-Diversity Framework and Archive Structure

Quality-diversity algorithms simultaneously optimize for both solution performance (fitness) and diversity across a discretized behavioral descriptor space. Formally, let $X\subseteq\mathbb{R}^d$ denote the genotype (parameter) space, $f:X\to\mathbb{R}$ the scalar fitness function, and $b:X\rightarrow\mathcal{B}\subseteq\mathbb{R}^k$ the behavioral descriptor mapping. The descriptor space $\mathcal{B}$ is discretized into $M$ cells, constructing an archive
$$ \mathcal{A} = \{A_i\;|\;i = 1,\ldots, M\}, $$
where $A_i$ stores the best-so-far individual $x$ for which $b(x)$ falls into cell $i$, or $\bot$ if empty. The fundamental QD objective is, for each $i$,
$$ A_i = \arg\max_{x\in X:\;b(x) \in \text{cell }i} f(x)\,. $$
Evaluation metrics include coverage $C = |\{i : A_i \neq \bot \}|$, QD-Score $Q = \sum_{i: A_i\neq\bot} f(A_i)$, and Max-Fitness $F_{\max} = \max_{i: A_i \neq \bot} f(A_i)$.

## 2. Heterogeneous Emitters: Principles and Mechanisms

Standard MAP-Elites employs a single, uniform variation operator, typically Gaussian mutation. By contrast, ME-MAP-Elites instantiates a pool of emitters, each guided by distinct search heuristics or local optimization strategies. This emitter diversity is central to improved QD performance.

Typical emitter types include [2007.05352]:
- **Optimizing emitters**: CMA-ES instances optimizing $f(x)$.
- **Random-direction emitters**: CMA-ES variants rewarding directional progress in descriptor space, i.e., $r(x) = \langle b(x)-b(\mu), d \rangle$ for random $d$.
- **Improvement emitters**: CMA-ES optimizing archive addition or quality improvement.
- **Random (MAP-Elites-style) emitters**: Direct random variations as in standard MAP-Elites.

Emitters propose candidate solutions via sampling and local adaptation, with their offspring evaluated for fitness and behavioral descriptor. Archive updates occur if a new individual either fills an empty cell or improves upon the incumbent.

## 3. Dynamic Emitter Selection: Bandit-Based Scheduling

Emitter allocation is handled dynamically via sliding-window, multiple-play UCB1 bandit algorithms. Over a window of $W$ generations, the empirical mean reward for emitter $e$, $\hat r_e = S_e / N_e$, combines with an exploration term, yielding index

Source: https://www.emergentmind.com/topics/multi-emitter-map-elites-me-map-elites