ICML 2021 论文列表

Two-player, constant-sum games are well studied in the literature, but there has been limited progress outside of this setting. We propose Joint Policy-Space Response Oracles (JPSRO), an algorithm for training agents in n-player, general-sum extensive form games, which provably converges to an equilibrium. We further suggest correlated equilibria (CE) as promising meta-solvers, and propose a novel solution concept Maximum Gini Correlated Equilibrium (MGCE), a principled and computationally efficient family of solutions for solving the correlated equilibrium selection problem. We conduct several experiments using CE meta-solvers for JPSRO and demonstrate convergence on n-player, general-sum games.

We propose a novel policy update that combines regularized policy optimization with model learning as an auxiliary loss. The update (henceforth Muesli) matches MuZero’s state-of-the-art performance on Atari. Notably, Muesli does so without using deep search: it acts directly with a policy network and has computation speed comparable to model-free baselines. The Atari results are complemented by extensive ablations, and by additional results on continuous control and 9x9 Go.

For the past century, the anatomy of a neuron has been considered one of its defining features: The shape of a neuron’s dendrites and axon fundamentally determines what other neurons it can connect to. These neurites have been described using mathematical tools e.g. in the context of cell type classification, but generative models of these structures have only rarely been proposed and are often computationally inefficient. Here we propose MorphVAE, a sequence-to-sequence variational autoencoder with spherical latent space as a generative model for neural morphologies. The model operates on walks within the tree structure of a neuron and can incorporate expert annotations on a subset of the data using semi-supervised learning. We develop our model on artificially generated toy data and evaluate its performance on dendrites of excitatory cells and axons of inhibitory cells of mouse motor cortex (M1) and dendrites of retinal ganglion cells. We show that the learned latent feature space allows for better cell type discrimination than other commonly used features. By sampling new walks from the latent space we can easily construct new morphologies with a specified degree of similarity to their reference neuron, providing an efficient generative model for neural morphologies.

Variational representations of $f$-divergences are central to many machine learning algorithms, with Lipschitz constrained variants recently gaining attention. Inspired by this, we define the Moreau-Yosida approximation of $f$-divergences with respect to the Wasserstein-$1$ metric. The corresponding variational formulas provide a generalization of a number of recent results, novel special cases of interest and a relaxation of the hard Lipschitz constraint. Additionally, we prove that the so-called tight variational representation of $f$-divergences can be to be taken over the quotient space of Lipschitz functions, and give a characterization of functions achieving the supremum in the variational representation. On the practical side, we propose an algorithm to calculate the tight convex conjugate of $f$-divergences compatible with automatic differentiation frameworks. As an application of our results, we propose the Moreau-Yosida $f$-GAN, providing an implementation of the variational formulas for the Kullback-Leibler, reverse Kullback-Leibler, $\chi^2$, reverse $\chi^2$, squared Hellinger, Jensen-Shannon, Jeffreys, triangular discrimination and total variation divergences as GANs trained on CIFAR-10, leading to competitive results and a simple solution to the problem of uniqueness of the optimal critic.

Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful and general conditional SI method for SFS using the homotopy method which enables us to overcome this limitation. The homotopy-based SI is especially effective for more complicated feature selection algorithms. As an example, we develop a conditional SI method for forward-backward SFS with AIC-based stopping criteria and show that it is not adversely affected by the increased complexity of the algorithm. We conduct several experiments to demonstrate the effectiveness and efficiency of the proposed method.

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. However, importance sampling is known to perform poorly in high dimensions. While it has been suggested many times in the literature to use more sophisticated algorithms such as Annealed Importance Sampling (AIS) and its Sequential Importance Sampling (SIS) extensions, the potential benefits brought by these advanced techniques have never been realized for VAE: the AIS estimate cannot be easily differentiated, while SIS requires the specification of carefully chosen backward Markov kernels. In this paper, we address both issues and demonstrate the performance of the resulting Monte Carlo VAEs on a variety of applications.

State-of-the-art deep reinforcement learning (DRL) algorithms tend to overfit due to the model discrepancy between source and target environments. Though applying domain randomization during training can improve the average performance by randomly generating a sufficient diversity of environments in simulator, the worst-case environment is still neglected without any performance guarantee. Since the average and worst-case performance are both important for generalization in RL, in this paper, we propose a policy optimization approach for concurrently improving the policy’s performance in the average and worst-case environment. We theoretically derive a lower bound for the worst-case performance of a given policy by relating it to the expected performance. Guided by this lower bound, we formulate an optimization problem to jointly optimize the policy and sampling distribution, and prove that by iteratively solving it the worst-case performance is monotonically improved. We then develop a practical algorithm, named monotonic robust policy optimization (MRPO). Experimental evaluations in several robot control tasks demonstrate that MRPO can generally improve both the average and worst-case performance in the source environments for training, and facilitate in all cases the learned policy with a better generalization capability in some unseen testing environments.

The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A simple way to circumvent this issue is to use reversible architectures. In this paper, we propose to change the forward rule of a ResNet by adding a momentum term. The resulting networks, momentum residual neural networks (MomentumNets), are invertible. Unlike previous invertible architectures, they can be used as a drop-in replacement for any existing ResNet block. We show that MomentumNets can be interpreted in the infinitesimal step size regime as second-order ordinary differential equations (ODEs) and exactly characterize how adding momentum progressively increases the representation capabilities of MomentumNets: they can learn any linear mapping up to a multiplicative factor, while ResNets cannot. In a learning to optimize setting, where convergence to a fixed point is required, we show theoretically and empirically that our method succeeds while existing invertible architectures fail. We show on CIFAR and ImageNet that MomentumNets have the same accuracy as ResNets, while having a much smaller memory footprint, and show that pre-trained MomentumNets are promising for fine-tuning models.

Many transfer problems require re-using previously optimal decisions for solving new tasks, which suggests the need for learning algorithms that can modify the mechanisms for choosing certain actions independently of those for choosing others. However, there is currently no formalism nor theory for how to achieve this kind of modular credit assignment. To answer this question, we define modular credit assignment as a constraint on minimizing the algorithmic mutual information among feedback signals for different decisions. We introduce what we call the modularity criterion for testing whether a learning algorithm satisfies this constraint by performing causal analysis on the algorithm itself. We generalize the recently proposed societal decision-making framework as a more granular formalism than the Markov decision process to prove that for decision sequences that do not contain cycles, certain single-step temporal difference action-value methods meet this criterion while all policy-gradient methods do not. Empirical evidence suggests that such action-value methods are more sample efficient than policy-gradient methods on transfer problems that require only sparse changes to a sequence of previously optimal decisions.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} – convex polytopes spanned by agents’ mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve at least the same, and in most games, lower exploitability than PSRO solvers by finding effective and diverse strategies.

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference (Bowman et al., 2015b) and ListOps (Nangia & Bowman, 2018). We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.

Balancing exploration and exploitation is crucial in reinforcement learning (RL). In this paper, we study model-based posterior sampling for reinforcement learning (PSRL) in continuous state-action spaces theoretically and empirically. First, we show the first regret bound of PSRL in continuous spaces which is polynomial in the episode length to the best of our knowledge. With the assumption that reward and transition functions can be modeled by Bayesian linear regression, we develop a regret bound of $\tilde{O}(H^{3/2}d\sqrt{T})$, where $H$ is the episode length, $d$ is the dimension of the state-action space, and $T$ indicates the total time steps. This result matches the best-known regret bound of non-PSRL methods in linear MDPs. Our bound can be extended to nonlinear cases as well with feature embedding: using linear kernels on the feature representation $\phi$, the regret bound becomes $\tilde{O}(H^{3/2}d_{\phi}\sqrt{T})$, where $d_\phi$ is the dimension of the representation space. Moreover, we present MPC-PSRL, a model-based posterior sampling algorithm with model predictive control for action selection. To capture the uncertainty in models, we use Bayesian linear regression on the penultimate layer (the feature representation layer $\phi$) of neural networks. Empirical results show that our algorithm achieves the state-of-the-art sample efficiency in benchmark continuous control tasks compared to prior model-based algorithms, and matches the asymptotic performance of model-free algorithms.

In a poisoning attack, an adversary who controls a small fraction of the training data attempts to select that data, so a model is induced that misbehaves in a particular way. We consider poisoning attacks against convex machine learning models and propose an efficient poisoning attack designed to induce a model specified by the adversary. Unlike previous model-targeted poisoning attacks, our attack comes with provable convergence to any attainable target model. We also provide a lower bound on the minimum number of poisoning points needed to achieve a given target model. Our method uses online convex optimization and finds poisoning points incrementally. This provides more flexibility than previous attacks which require an a priori assumption about the number of poisoning points. Our attack is the first model-targeted poisoning attack that provides provable convergence for convex models. In our experiments, it either exceeds or matches state-of-the-art attacks in terms of attack success rate and distance to the target model.

When decision-makers can directly intervene, policy evaluation algorithms give valid causal estimates. In off-policy evaluation (OPE), there may exist unobserved variables that both impact the dynamics and are used by the unknown behavior policy. These “confounders” will introduce spurious correlations and naive estimates for a new policy will be biased. We develop worst-case bounds to assess sensitivity to these unobserved confounders in finite horizons when confounders are drawn iid each period. We demonstrate that a model-based approach with robust MDPs gives sharper lower bounds by exploiting domain knowledge about the dynamics. Finally, we show that when unobserved confounders are persistent over time, OPE is far more difficult and existing techniques produce extremely conservative bounds.

In this paper we consider the problem of learning an $\epsilon$-optimal policy for a discounted Markov Decision Process (MDP). Given an MDP with $S$ states, $A$ actions, the discount factor $\gamma \in (0,1)$, and an approximation threshold $\epsilon > 0$, we provide a model-free algorithm to learn an $\epsilon$-optimal policy with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{\epsilon^2(1-\gamma)^{5.5}})$ \footnote{In this work, the notation $\tilde{O}(\cdot)$ hides poly-logarithmic factors of $S,A,1/(1-\gamma)$, and $1/\epsilon$.} and success probability $(1-p)$. For small enough $\epsilon$, we show an improved algorithm with sample complexity $\tilde{O}(\frac{SA\ln(1/p)}{\epsilon^2(1-\gamma)^{3}})$. While the first bound improves upon all known model-free algorithms and model-based ones with tight dependence on $S$, our second algorithm beats all known sample complexity bounds and matches the information theoretic lower bound up to logarithmic factors.

The ability to plan into the future while utilizing only raw high-dimensional observations, such as images, can provide autonomous agents with broad and general capabilities. However, realistic tasks require performing temporally extended reasoning, and cannot be solved with only myopic, short-sighted planning. Recent work in model-based reinforcement learning (RL) has shown impressive results on tasks that require only short-horizon reasoning. In this work, we study how the long-horizon planning abilities can be improved with an algorithm that optimizes over sequences of states, rather than actions, which allows better credit assignment. To achieve this, we draw on the idea of collocation and adapt it to the image-based setting by leveraging probabilistic latent variable models, resulting in an algorithm that optimizes trajectories over latent variables. Our latent collocation method (LatCo) provides a general and effective visual planning approach, and significantly outperforms prior model-based approaches on challenging visual control tasks with sparse rewards and long-term goals. See the videos on the supplementary website \url{https://sites.google.com/view/latco-mbrl/.}

Real-world machine learning systems are often trained using a mix of data sources with varying cost and quality. Understanding how the size and composition of a training dataset affect model performance is critical for advancing our understanding of generalization, as well as designing more effective data collection policies. We show that there is a simple scaling law that predicts the loss incurred by a model even under varying dataset composition. Our work expands recent observations of scaling laws for log-linear generalization error in the i.i.d setting and uses this to cast model performance prediction as a learning problem. Using the theory of optimal experimental design, we derive a simple rational function approximation to generalization error that can be fitted using a few model training runs. Our approach can achieve highly accurate ($r^2\approx .9$) predictions of model performance under substantial extrapolation in two different standard supervised learning tasks and is accurate ($r^2 \approx .83$) on more challenging machine translation and question answering tasks where many baselines achieve worse-than-random performance.

Production systems operating on a growing domain of analytic services often require generating warm-start solution models for emerging tasks with limited data. One potential approach to address this warm-start challenge is to adopt meta learning to generate a base model that can be adapted to solve unseen tasks with minimal fine-tuning. This however requires the training processes of previous solution models of existing tasks to be synchronized. This is not possible if these models were pre-trained separately on private data owned by different entities and cannot be synchronously re-trained. To accommodate for such scenarios, we develop a new personalized learning framework that synthesizes customized models for unseen tasks via fusion of independently pre-trained models of related tasks. We establish performance guarantee for the proposed framework and demonstrate its effectiveness on both synthetic and real datasets.

Data-driven pricing strategies are becoming increasingly common, where customers are offered a personalized price based on features that are predictive of their valuation of a product. It is desirable for this pricing policy to be simple and interpretable, so it can be verified, checked for fairness, and easily implemented. However, efforts to incorporate machine learning into a pricing framework often lead to complex pricing policies that are not interpretable, resulting in slow adoption in practice. We present a novel, customized, prescriptive tree-based algorithm that distills knowledge from a complex black-box machine learning algorithm, segments customers with similar valuations and prescribes prices in such a way that maximizes revenue while maintaining interpretability. We quantify the regret of a resulting policy and demonstrate its efficacy in applications with both synthetic and real-world datasets.