We present a novel method for learning a set of disentangled reward functions that sum to the original environment reward and are constrained to be independently obtainable. We define independent obtainability in terms of value functions with respect to obtaining one learned reward while pursuing another learned reward. Empirically, we illustrate that our method can learn meaningful reward decompositions in a variety of domains and that these decompositions exhibit some form of generalization performance when the environment's reward is modified. Theoretically, we derive results about the effect of maximizing our method's objective on the resulting reward functions and their corresponding optimal policies.
Some methods seek robust interpretable disentangled features @cite_3 @cite_2 @cite_0 @cite_4 . For example, does so by creating an information bottleneck'' @cite_7 that pressures the latent representation to be unit Gaussian. accomplishes a similar goal by maximizing the mutual information between components of their latent representation and other independent random variables. Methods such as these have been leveraged in RL to decompose the state of the environment. In particular, have applied @math -VAE to learn disentangled, modular'' representations of the environment state for use in many goals RL @cite_1 .
@cite_4 @cite_7 @cite_1 @cite_3 @cite_0 @cite_2
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Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a two-level hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the trade-offs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors. Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks, interpretability, etc. We consider the problem of unsupervised learning of disentangled representations from large pool of unlabeled observations, and propose a variational inference based approach to infer disentangled latent factors. We introduce a regularizer on the expectation of the approximate posterior over observed data that encourages the disentanglement. We evaluate the proposed approach using several quantitative metrics and empirically observe significant gains over existing methods in terms of both disentanglement and data likelihood (reconstruction quality). We would like to learn a representation of the data which decomposes an observation into factors of variation which we can independently control. Specifically, we want to use minimal supervision to learn a latent representation that reflects the semantics behind a specific grouping of the data, where within a group the samples share a common factor of variation. For example, consider a collection of face images grouped by identity. We wish to anchor the semantics of the grouping into a relevant and disentangled representation that we can easily exploit. However, existing deep probabilistic models often assume that the observations are independent and identically distributed. We present the Multi-Level Variational Autoencoder (ML-VAE), a new deep probabilistic model for learning a disentangled representation of a set of grouped observations. The ML-VAE separates the latent representation into semantically meaningful parts by working both at the group level and the observation level, while retaining efficient test-time inference. Quantitative and qualitative evaluations show that the ML-VAE model (i) learns a semantically meaningful disentanglement of grouped data, (ii) enables manipulation of the latent representation, and (iii) generalises to unseen groups. We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our @math -TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art @math -VAE objective for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the latent variables model is trained using our framework.