ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANs
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assumption of convex-concavity, guided by a continuous-time analysis with differential equations. First, we show that simGD, as is, converges with stochastic sub-gradients under strict convexity in the primal variable. Second, we generalize optimistic simGD to accommodate an optimism rate separate from the learning rate and show its convergence with full gradients. Finally, we present anchored simGD, a new method, and show convergence with stochastic subgradients.
This paper analyzes the dynamics of stochastic gradient descent when applied to convex-concave games (motivated by the game used to train GANs, which is typically not convex-concave), as well as the previously proposed GD with optimism and a new anchored GD algorithm that provably converges under weaker assumptions than SGD or SGD with optimism. This seems like a nice contribution to the GAN theory literature, and the anchored SSSGD algorithm might well have significant practical value (although more thorough experiments would be needed to make this claim). As such I recommend acceptance. The obvious critique to raise of this kind of work is that the GAN problems that motivate it are clearly not convex-concave, and so it is unclear how or whether the results can or should inform practice. The simplest way to make the case for that kind of relevance is empirically, so I*d recommend that the authors consider what kinds of GAN experiments would support (or falsify) the claim that their theoretical results have some hope of generalizing to the non-convex-concave setting. Figure 4 is suggestive, but it doesn*t say much except that anchored Adam might occasionally be a good choice (and sometimes isn*t). The samples in Figure 3 are pretty far from the state of the art, and in any case Figure 3 doesn*t even say which training method generated them. Finally, PLEASE don*t include acknowledgments in a paper that*s under double-blind review; it compromises your anonymity, which in principle could be grounds for a desk rejection.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANs
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assumption of convex-concavity, guided by a continuous-time analysis with differential equations. First, we show that simGD, as is, converges with stochastic sub-gradients under strict convexity in the primal variable. Second, we generalize optimistic simGD to accommodate an optimism rate separate from the learning rate and show its convergence with full gradients. Finally, we present anchored simGD, a new method, and show convergence with stochastic subgradients.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper analyzes the dynamics of stochastic gradient descent when applied to convex-concave games (motivated by the game used to train GANs, which is typically not convex-concave), as well as the previously proposed GD with optimism and a new anchored GD algorithm that provably converges under weaker assumptions than SGD or SGD with optimism. This seems like a nice contribution to the GAN theory literature, and the anchored SSSGD algorithm might well have significant practical value (although more thorough experiments would be needed to make this claim). As such I recommend acceptance. The obvious critique to raise of this kind of work is that the GAN problems that motivate it are clearly not convex-concave, and so it is unclear how or whether the results can or should inform practice. The simplest way to make the case for that kind of relevance is empirically, so I*d recommend that the authors consider what kinds of GAN experiments would support (or falsify) the claim that their theoretical results have some hope of generalizing to the non-convex-concave setting. Figure 4 is suggestive, but it doesn*t say much except that anchored Adam might occasionally be a good choice (and sometimes isn*t). The samples in Figure 3 are pretty far from the state of the art, and in any case Figure 3 doesn*t even say which training method generated them. Finally, PLEASE don*t include acknowledgments in a paper that*s under double-blind review; it compromises your anonymity, which in principle could be grounds for a desk rejection.
assistant
This paper analyzes the dynamics of stochastic gradient descent when applied to convex-concave games (motivated by the game used to train GANs, which is typically not convex-concave), as well as the previously proposed GD with optimism and a new anchored GD algorithm that provably converges under weaker assumptions than SGD or SGD with optimism. This seems like a nice contribution to the GAN theory literature, and the anchored SSSGD algorithm might well have significant practical value (although more thorough experiments would be needed to make this claim). As such I recommend acceptance. The obvious critique to raise of this kind of work is that the GAN problems that motivate it are clearly not convex-concave, and so it is unclear how or whether the results can or should inform practice. The simplest way to make the case for that kind of relevance is empirically, so I*d recommend that the authors consider what kinds of GAN experiments would support (or falsify) the claim that their theoretical results have some hope of generalizing to the non-convex-concave setting. Figure 4 is suggestive, but it doesn*t say much except that anchored Adam might occasionally be a good choice (and sometimes isn*t). The samples in Figure 3 are pretty far from the state of the art, and in any case Figure 3 doesn*t even say which training method generated them. Finally, PLEASE don*t include acknowledgments in a paper that*s under double-blind review; it compromises your anonymity, which in principle could be grounds for a desk rejection.