# Inverse Learning

Aliases Cost Function Learning

https://phillipi.github.io/pix2pix/ Image-to-Image Translation with Conditional Adversarial Nets

We investigate conditional adversarial networks as a
general-purpose solution to image-to-image translation
problems. These networks not only learn the mapping from
input image to output image, but also learn a loss function
to train this mapping. **This makes it possible to apply
the same generic approach to problems that traditionally
would require very different loss formulations.** We demonstrate
that this approach is effective at synthesizing photos
from label maps, reconstructing objects from edge maps,
and colorizing images, among other tasks. **As a community,
we no longer hand-engineer our mapping functions,
and this work suggests we can achieve reasonable results
without hand-engineering our loss functions either.**

Coming up with loss functions that force the CNN to do what we really want – e.g., output sharp, realistic images – is an open problem and generally requires expert knowledge.

GANs learn a loss that tries to classify if the output image is real or fake, while simultaneously training a generative model to minimize this loss. Because GANs learn a loss that adapts to the data, they can be applied to a multitude of tasks that traditionally would require very different kinds of loss functions.

In this paper, we explore GANs in the conditional setting. Just as GANs learn a generative model of data, conditional GANs (cGANs) learn a conditional generative model.

https://www.semanticscholar.org/paper/Conditional-Generative-Adversarial-Nets-Mirza-Osindero/ba753286b9e2f32c5d5a7df08571262e257d2e53 Conditional Generative Adversarial Nets

In this work we introduce the conditional version of generative adversarial nets, which can be constructed by simply feeding the data, y, we wish to condition on to both the generator and discriminator. We show that this model can generate MNIST digits conditioned on class labels. We also illustrate how this model could be used to learn a multi-modal model, and provide preliminary examples of an application to image tagging in which we demonstrate how this approach can generate descriptive tags which are not part of training labels.

http://www.yingzhenli.net/home/blog/?p=421 GANs, mutual information, and possibly algorithm selection?

https://arxiv.org/abs/1511.05101 How (not) to Train your Generative Model: Scheduled Sampling, Likelihood, Adversary?

We argue that maximum likelihood is an inappropriate training objective when the end-goal is to generate natural-looking samples. We go on to derive an ideal objective function to use in this situation instead. We introduce a generalisation of adversarial training, and show how such method can interpolate between maximum likelihood training and our ideal training objective. To our knowledge this is the first theoretical analysis that explains why adversarial training tends to produce samples with higher perceived quality.

Our findings and recommendations can be summarised as follows:

1. Maximum likelihood should not be used as the training objective if the end goal is to draw realistic samples from the model. Models trained via maximum likelhiood have a tendency to overgeneralise and generate unplausible samples.

2. Scheduled sampling, designed to overcome the shortcomings of maximum likelihood, fails to address the fundamental problems, and we showed it is an inconsistent training strategy.

3. We theorise that KL[QkP] could be used as an idealised objective function to describe the no-reference perceptual quality assessment scenario, but it is impractical to use in practice.

4. We propose the generalised Jensen-Shannon divergence as a promising, more tractable objective function that can effectively interpolate between maximum likelihood and KL[QkP]-minimisation.

5. Our analysis suggests that adversarial training strategies are a the best choice for generative modelling, and we propose a more flexible algorithm based on our generalised JS divergence.

https://statpacking.wordpress.com/2015/01/04/upper-bounds-for-mutual-information/

https://arxiv.org/abs/1610.04490 Amortised MAP Inference for Image Super-resolution

MAP inference is often performed via optimisation-based iterative algorithms which don't compare well with the efficiency of neural-network-based alternatives. Here we introduce new methods for amortised MAP inference whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models.

https://arxiv.org/pdf/1611.03852v2.pdf A Connection Between Generative Adversarial Networks, Inverse Reinforcement Learning, and Energy-Based Models

In particular, we demonstrate an equivalence between a sample-based algorithm for maximum entropy IRL and a GAN in which the generator’s density can be evaluated and is provided as an additional input to the discriminator. Interestingly, maximum entropy IRL is a special case of an energy-based model.

https://arxiv.org/pdf/1612.00429v1.pdf Generalizing Skills with Semi-Supervised Reinforcement Learning

Can we make use of this limited supervision, and still benefit from the breadth of experience an agent might collect on its own? In this paper, we formalize this problem as semisupervised reinforcement learning, where the reward function can only be evaluated in a set of “labeled” MDPs, and the agent must generalize its behavior to the wide range of states it might encounter in a set of “unlabeled” MDPs, by using experience from both settings. Our proposed method infers the task objective in the unlabeled MDPs through an algorithm that resembles inverse RL, using the agent's own prior experience in the labeled MDPs as a kind of demonstration of optimal behavior. We evaluate our method on challenging tasks that require control directly from images, and show that our approach can improve the generalization of a learned deep neural network policy by using experience for which no reward function is available. We also show that our method outperforms direct supervised learning of the reward.

https://www.youtube.com/watch?v=Ts-nTIYDXok Cooperative Inverse Reinforcement Learning

https://arxiv.org/abs/1612.01397v1 Implicit Modeling – A Generalization of Discriminative and Generative Approaches

We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions. The proposed scheme combines the advantages of both worlds – it can use powerful complex discriminative models as its parts, having at the same time better generalization capabilities. We thoroughly evaluate the proposed method for a simple classification task with artificial data and illustrate its advantages for real-word scenarios on a semantic image segmentation problem.

https://arxiv.org/abs/1612.04318v1 Incorporating Human Domain Knowledge into Large Scale Cost Function Learning

While pure learning from demonstrations in the framework of Inverse Reinforcement Learning (IRL) is a promising approach, we can benefit from well informed human priors and incorporate them into the learning process. Our work achieves this by pretraining a model to regress to a manual cost function and refining it based on Maximum Entropy Deep Inverse Reinforcement Learning. When injecting prior knowledge as pretraining for the network, we achieve higher robustness, more visually distinct obstacle boundaries, and the ability to capture instances of obstacles that elude models that purely learn from demonstration data. Furthermore, by exploiting these human priors, the resulting model can more accurately handle corner cases that are scarcely seen in the demonstration data, such as stairs, slopes, and underpasses.

https://openreview.net/pdf?id=HkSOlP9lg Recurrent Inference Machines for Solving Inverse Problems

We propose a novel learning framework which abandons the dichotomy between model and inference. Instead, we introduce Recurrent Inference Machines (RIM), a class of recurrent neural networks (RNN) that directly learn to solve inverse problems.

https://arxiv.org/pdf/1606.03476.pdf Generative Adversarial Imitation Learning

Consider learning a policy from example expert behavior, without interaction
with the expert or access to reinforcement signal. One approach is to recover the
expert’s cost function with inverse reinforcement learning, then extract a policy
from that cost function with reinforcement learning. This approach is indirect
and can be slow. **We propose a new general framework for directly extracting a
policy from data, as if it were obtained by reinforcement learning following inverse
reinforcement learning. We show that a certain instantiation of our framework
draws an analogy between imitation learning and generative adversarial networks,
from which we derive a model-free imitation learning algorithm that obtains significant
performance gains over existing model-free methods in imitating complex
behaviors in large, high-dimensional environments.**

https://arxiv.org/abs/1605.09782 Adversarial Feature Learning

However, in their existing form, GANs have no means of learning the inverse mapping – projecting data back into the latent space. We propose Bidirectional Generative Adversarial Networks (BiGANs) as a means of learning this inverse mapping, and demonstrate that the resulting learned feature representation is useful for auxiliary supervised discrimination tasks, competitive with contemporary approaches to unsupervised and self-supervised feature learning.

https://arxiv.org/abs/1703.09912v1 One Network to Solve Them All — Solving Linear Inverse Problems using Deep Projection Models

We propose a general framework to train a single deep neural network that solves arbitrary linear inverse problems. The proposed network acts as a proximal operator for an optimization algorithm and projects non-image signals onto the set of natural images defined by the decision boundary of a classifier.

https://arxiv.org/pdf/1606.03137v2.pdf Cooperative Inverse Reinforcement Learning

For an autonomous system to be helpful to humans and to pose no unwarranted risks, it needs to align its values with those of the humans in its environment in such a way that its actions contribute to the maximization of value for the humans. We propose a formal definition of the value alignment problem as cooperative inverse reinforcement learning (CIRL). A CIRL problem is a cooperative, partialinformation game with two agents, human and robot; both are rewarded according to the human’s reward function, but the robot does not initially know what this is. In contrast to classical IRL, where the human is assumed to act optimally in isolation, optimal CIRL solutions produce behaviors such as active teaching, active learning, and communicative actions that are more effective in achieving value alignment. We show that computing optimal joint policies in CIRL games can be reduced to solving a POMDP, prove that optimality in isolation is suboptimal in CIRL, and derive an approximate CIRL algorithm.

https://arxiv.org/abs/1707.00372 Deep Convolutional Framelets: A General Deep Learning for Inverse Problems

This discovery reveals the limitations of many existing deep learning architectures for inverse problems, and leads us to propose a novel deep convolutional framelets neural network.

https://arxiv.org/abs/1708.07738 A Function Approximation Method for Model-based High-Dimensional Inverse Reinforcement Learning

This works handles the inverse reinforcement learning problem in high-dimensional state spaces, which relies on an efficient solution of model-based high-dimensional reinforcement learning problems. To solve the computationally expensive reinforcement learning problems, we propose a function approximation method to ensure that the Bellman Optimality Equation always holds, and then estimate a function based on the observed human actions for inverse reinforcement learning problems. The time complexity of the proposed method is linearly proportional to the cardinality of the action set, thus it can handle high-dimensional even continuous state spaces efficiently. We test the proposed method in a simulated environment to show its accuracy, and three clinical tasks to show how it can be used to evaluate a doctor's proficiency.

https://arxiv.org/pdf/1706.04008.pdf Recurrent Inference Machines for Solving Inverse Problems

We propose a learning framework, called Recurrent Inference Machines (RIM), in which we turn algorithm construction the other way round: Given data and a task, train an RNN to learn an inference algorithm. Because RNNs are Turing complete [1, 2] they are capable to implement any inference algorithm. The framework allows for an abstraction which removes the need for domain knowledge. We demonstrate in several image restoration experiments that this abstraction is effective, allowing us to achieve state-of-the-art performance on image denoising and super-resolution tasks and superior across-task generalization.

https://arxiv.org/abs/1711.02827 Inverse Reward Design

Autonomous agents optimize the reward function we give them. What they don’t know is how hard it is for us to design a reward function that actually captures what we want. When designing the reward, we might think of some specific training scenarios, and make sure that the reward will lead to the right behavior in those scenarios. Inevitably, agents encounter new scenarios (e.g., new types of terrain) where optimizing that same reward may lead to undesired behavior. Our insight is that reward functions are merely observations about what the designer actually wants, and that they should be interpreted in the context in which they were designed. We introduce inverse reward design (IRD) as the problem of inferring the true objective based on the designed reward and the training MDP. We introduce approximate methods for solving IRD problems, and use their solution to plan risk-averse behavior in test MDPs. Empirical results suggest that this approach can help alleviate negative side effects of misspecified reward functions and mitigate reward hacking.

https://arxiv.org/abs/1802.04821v1 Evolved Policy Gradients

We propose a meta-learning approach for learning gradient-based reinforcement learning (RL) algorithms. The idea is to evolve a differentiable loss function, such that an agent, which optimizes its policy to minimize this loss, will achieve high rewards. The loss is parametrized via temporal convolutions over the agent's experience. Because this loss is highly flexible in its ability to take into account the agent's history, it enables fast task learning and eliminates the need for reward shaping at test time. Empirical results show that our evolved policy gradient algorithm achieves faster learning on several randomized environments compared to an off-the-shelf policy gradient method. Moreover, at test time, our learner optimizes only its learned loss function, and requires no explicit reward signal. In effect, the agent internalizes the reward structure, suggesting a direction toward agents that learn to solve new tasks simply from intrinsic motivation.

https://arxiv.org/abs/1805.12573 Learning a Prior over Intent via Meta-Inverse Reinforcement Learning

A significant challenge for the practical application of reinforcement learning in the real world is the need to specify an oracle reward function that correctly defines a task. Inverse reinforcement learning (IRL) seeks to avoid this challenge by instead inferring a reward function from expert behavior. While appealing, it can be impractically expensive to collect datasets of demonstrations that cover the variation common in the real world (e.g. opening any type of door). Thus in practice, IRL must commonly be performed with only a limited set of demonstrations where it can be exceedingly difficult to unambiguously recover a reward function. In this work, we exploit the insight that demonstrations from other tasks can be used to constrain the set of possible reward functions by learning a “prior” that is specifically optimized for the ability to infer expressive reward functions from limited numbers of demonstrations. We demonstrate that our method can efficiently recover rewards from images for novel tasks and provide intuition as to how our approach is analogous to learning a prior.

https://hci.iwr.uni-heidelberg.de/vislearn/inverse-problems-invertible-neural-networks/ Analyzing Inverse Problems with Invertible Neural Networks

https://arxiv.org/abs/1808.04730 Analyzing Inverse Problems with Invertible Neural Networks

. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.

https://arxiv.org/abs/1809.03060 Active Inverse Reward Design

Inverse reward design (IRD) is a preference inference method that infers a true reward function from an observed, possibly misspecified, proxy reward function. This allows the system to determine when it should trust its observed reward function and respond appropriately. This has been shown to avoid problems in reward design such as negative side-effects (omitting a seemingly irrelevant but important aspect of the task) and reward hacking (learning to exploit unanticipated loopholes). In this paper, we actively select the set of proxy reward functions available to the designer. This improves the quality of inference and simplifies the associated reward design problem. We present two types of queries: discrete queries, where the system designer chooses from a discrete set of reward functions, and feature queries, where the system queries the designer for weights on a small set of features. We evaluate this approach with experiments in a personal shopping assistant domain and a 2D navigation domain. We find that our approach leads to reduced regret at test time compared with vanilla IRD. Our results indicate that actively selecting the set of available reward functions is a promising direction to improve the efficiency and effectiveness of reward design.

https://xbpeng.github.io/projects/VDB/index.html Variational Discriminator Bottleneck: Improving Imitation Learning, Inverse RL, and GANs by Constraining Information Flow

https://arxiv.org/pdf/1804.09160.pdf No Metrics Are Perfect: Adversarial Reward Learning for Visual Storytelling

we propose an Adversarial REward Learning (AREL) framework to learn an implicit reward function from human demonstrations, and then optimize policy search with the learned reward function. Though automatic evaluation indicates slight performance boost over state-of-the-art (SOTA) methods in cloning expert behaviors, human evaluation shows that our approach achieves significant improvement in generating more human-like stories than SOTA systems.

https://arxiv.org/abs/1706.04008 Recurrent Inference Machines for Solving Inverse Problems

We establish this framework by abandoning the traditional separation between model and inference. Instead, we propose to learn both components jointly without the need to define their explicit functional form. This paradigm shift enables us to bridge the gap between the fields of deep learning and inverse problems. A crucial and unique quality of RIMs are their ability to generalize across tasks without the need to retrain. We convincingly demonstrate this feature in our experiments as well as state of the art results on image denoising and super-resolution.