Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number $N$ of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as $N$ increases. Moreover, our complexity analysis provides a theoretical quantification on the improved efficiency of ANIL over MAML.

We further extend Kaleidoscope to critic ensembles in the context of actor-critic algorithms, which could help improve value estimations.

Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number N of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as N increases.

Weaknesses: - It is not very clear about the evaluation for outer iterations. Is the number of aggregated tasks affecting the convergence too? In MAML, the gradient for outer-loop is computed based on the inner-loop of several tasks. Particularly, the number of samples in the support set and the query set (on mini-ImageNet) may affect the error and the convergence. Fallah et al. [4] considers this number of samples in the inner-loop to their analysis.

This paper studies the convergence rate and computational complexity of ANIL (a variant of MAML) for cases of strongly-convex and nonconvex inner-loop loss. The paper focuses on an important problem (due to increasing interest in MAML type methods) and it empirically backups its theoretical claims. There were some concerns initially, specially those raised by R4 (providing no insight into improving the existing methods, discrepancy between optimization methods in theoretical analysis and empirical verification). However, authors' response was very helpful and at the end all reviewers agree that the submission is ready for publication. I strongly recommend authors' to incorporate R1's post rebuttal comment in the final version of this work, as it can be an important and yet easy to add component. I am referring to R1's request: " a simple theoretical example, such as a 1-dimensional quadratic objective, could elaborate on the tightness.

In multi-agent reinforcement learning (MARL), parameter sharing is commonly employed to enhance sample efficiency. However, the popular approach of full parameter sharing often leads to homogeneous policies among agents, potentially limiting the performance benefits that could be derived from policy diversity. To address this critical limitation, we introduce \emph{Kaleidoscope}, a novel adaptive partial parameter sharing scheme that fosters policy heterogeneity while still maintaining high sample efficiency. Specifically, Kaleidoscope maintains one set of common parameters alongside multiple sets of distinct, learnable masks for different agents, dictating the sharing of parameters. It promotes diversity among policy networks by encouraging discrepancy among these masks, without sacrificing the efficiencies of parameter sharing. This design allows Kaleidoscope to dynamically balance high sample efficiency with a broad policy representational capacity, effectively bridging the gap between full parameter sharing and non-parameter sharing across various environments. We further extend Kaleidoscope to critic ensembles in the context of actor-critic algorithms, which could help improve value estimations.Our empirical evaluations across extensive environments, including multi-agent particle environment, multi-agent MuJoCo and StarCraft multi-agent challenge v2, demonstrate the superior performance of Kaleidoscope compared with existing parameter sharing approaches, showcasing its potential for performance enhancement in MARL. The code is publicly available at \url{https://github.com/LXXXXR/Kaleidoscope}.

Although model-agnostic meta-learning (MAML) is a very successful algorithm in meta-learning practice, it can have high computational cost because it updates all model parameters over both the inner loop of task-specific adaptation and the outer-loop of meta initialization training. A more efficient algorithm ANIL (which refers to almost no inner loop) was proposed recently by Raghu et al. 2019, which adapts only a small subset of parameters in the inner loop and thus has substantially less computational cost than MAML as demonstrated by extensive experiments. However, the theoretical convergence of ANIL has not been studied yet. In this paper, we characterize the convergence rate and the computational complexity for ANIL under two representative inner-loop loss geometries, i.e., strongly-convexity and nonconvexity. Our results show that such a geometric property can significantly affect the overall convergence performance of ANIL. For example, ANIL achieves a faster convergence rate for a strongly-convex inner-loop loss as the number N of inner-loop gradient descent steps increases, but a slower convergence rate for a nonconvex inner-loop loss as N increases.