czxttkl

Some update before we dive into today’s topic: I have not updated this blog for about 2 months, which is considered a long time : ). This is because I have picked up more tech lead work for setting up the team’s planning. I sincerely hope that our team will steer towards a good direction from 2022 and beyond. 

Now, let’s go to today’s topic: normalizing flows. Normalizing flows is a type of generative models. Generative models can be best summarized using the following objective function: 

i.e., we want to find a model which has the highest likelihood for the data generated from the data distribution as such to “approximate” the data distribution. 

According to [1] (starting 11:00 min), we can categorize generative models as:

1. Explicit with tractable density. i.e., has an analytical form. Examples include Normalizing Flows, PixelCNN, PixelRNN, and WaveNet. The latter three examples are autoregressive models which generate elements (e.g., pixels, audio clips) sequentially however are computationally heavy due to the nature of autoregressive. Normalizing Flows can generate the whole image instantaneously thus has a computational advantage over others. (For more pros/cons of Normalizing Flows, please refer to [4])
2. Explicit with approximate density, i.e., we are only optimizing for some bounds of . One example is Variational Encoder Decoder [2], in which we optimize ELBO. 
3. Implicit with no modeling of density. One example is Generative Adversarial Network (GAN), where we generate images just based on the generator network with a noise input. 

Normalizing Flows is based on a theory called “change of variables” [3]. Suppose and are random variables both with dimension . Also, suppose there is a mapping function such that and . Then the density functions of and have the following relationship:

,
where the last two equations are due to . From now on, we assume that denotes data while denotes a random variable in a latent space. 

In Normalizing Flows, the mapping is parameterized by (i.e., and ), which is what we try to learn. The objective function for learning becomes:

As you can see, our goal is to learn to map complex data distribution into a simpler latent variable distribution (usually ). The reason that we want to follow a simple distribution is that: first, we need to compute in the objective function so ideally should be easy to compute; second, once we learn , we know the mapping and , and then we can easily sample and apply to generate new data (e.g., new images). The requirement for a valid and practical is that: (1) it has an invertible ; (2) or is efficient to compute. 

One nice property of Normalizing Flows is that you can chain multiple transformation to form a new transformation. Suppose with each having a tractable inverse and a tractable Jacobian determinant. Then:

, where . 

In practice, we usually pick and optimize for log likelihood. Therefore, our objective becomes (as can be seen in Eqn. 1 from the Flow++ paper (one SOTA flow model) [5]): 

[6] provides a good tutorial for getting started in Normalizing Flows, while [7] has a more in-depth explanation and it will help a lot in understanding more advanced implementation such as Flow++ [8]. For now, I am going to introduce [6].

[6] introduces a flow called Planar Flow. It has relatively a straightforward transformation (linear + activation) and easy-to-compute Jacobian determinant:

Planar Flow is defined in Python as below:

Once it is defined, we can instantiate an arbitrary Planar Flow and see how it transforms from a 2D Normal distribution:

Now, suppose we want to learn what is the Planar Flow that could transform a 2D normal distribution to a target distribution defined as:

The objective function, as we already introduced above, is . Here, is samples from a 2D normal distribution, is the target density_ring distribution. Therefore, the loss function (to be minimized) is defined as:

The overall training loop is:

 

Last, I highly recommend watching this ECCV tutorial: https://www.youtube.com/watch?v=u3vVyFVU_lI

 

TODO:

dequantization:

https://uvadlc-notebooks.readthedocs.io/en/latest/tutorial_notebooks/tutorial11/NF_image_modeling.html#Dequantization

https://arxiv.org/pdf/1511.01844.pdf

 

 

References

[1] PixelCNN, Wavenet & Variational Autoencoders – Santiago Pascual – UPC 2017 https://www.youtube.com/watch?v=FeJT8ejgsL0

[2] Optimization with discrete random variables: https://czxttkl.com/2020/04/06/optimization-with-discrete-random-variables/

[3] Normalizing Flows note: https://deepgenerativemodels.github.io/notes/flow/

[4] Introduction to Normalizing Flows: https://towardsdatascience.com/introduction-to-normalizing-flows-d002af262a4b

[5] Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design: https://arxiv.org/abs/1902.00275

[6] Normalizing Flows in PyTorch: https://github.com/acids-ircam/pytorch_flows/blob/master/flows_01.ipynb

[7] UvA DL Notebook: https://uvadlc-notebooks.readthedocs.io/en/latest/tutorial_notebooks/tutorial11/NF_image_modeling.html

[8] Flow++ Github implementation: https://github.com/chrischute/flowplusplus

 

 

 

 

It has been some time since I got touch in neural architecture search (NAS) in my PhD, when I tried to get ideas for solving a combinatorial optimization problem for collectible card games’ deck recommendation. My memory about NAS mainly stays in one of the most classic NAS paper “Neural architecture search with reinforcement learning” [1], which uses policy gradient to search for better architectures. Apparently, things have advanced rapidly.

We can start from the most powerful NAS variant, AutoML-Zero [2]. It is not simply evolving an architecture, but actually evolve programs, literally. A program is defined with three main functions, setup(), learn(), and predict(). The algorithm uses evolutionary algorithms to search all possible implementations of the three functions using elementary operations. The objective of evolutionary algorithms is Evaluate() function shown below:

The evolutionary process is best illustrated in the following diagram:

After seeing one of the most advanced NAS development, we can look at simpler ones. EfficientNet shows that deep neural networks can improve the most performance when depth, width, and resolution are scaled up simultaneously. This is a million-dollar-worth finding! Hence, they propose compound scaling, where they simply search over one dimension :

They show that scaling existing models like MobileNet and ResNet up lead to better performance then scaling one dimension (width, depth, resolution).

Next, they scale up a baseline model EfficientNet-B0, a model found by MnasNet [4]. As we can see, scaling up MnasNet leads to steady improvement in performance. MnasNet is also a policy gradient-based NAS algorithm, similar to earlier works like [1] (which might not be sample efficient). But it has two main improvements: (1) the reward adds latency penalty; (2) each block is repeating one sub-architectures and different blocks could have different sub-architectures; as comparison, previous works repeat only one sub-architectures in multiple blocks. 

Besides EfficientNet, another simple yet effective method is using random search over a predictor that is trained on different possible architectures for predicting their performance (Neural Predictor from [5]). The predictor itself uses graph neural networks (specifically, graph convolutional network) to consume neural architectures represented as graphs. Most graph neural networks learn to represent node embeddings. However, in this work, they are interested in a regression model which maps the overall graph structure (architecture) to a scalar (performance), so they average the node embeddings to represent the overall graph’s embedding as the regression model’s input. 

The ancestor of Neural Predictor is PNAS [9], which progressively expands architectures. At each step of expansion, it queries a trained predictor for which block to expand. The predictor is trained on (architecture of blocks, performance), while it is used to predict the performance of architectures of blocks. PNAS cannot be fully parallelizable because of its progressive nature. That is one downside compared to Neural Predictor.

Now, let’s move on to one-shot NAS, which mostly revolve around the weight sharing technique. We use One-Shot [10], DARTS [11], and ProxylessNAS [8] to introduce the weight sharing technique. Weight sharing uses a much bigger architecture for training a model. The larger architecture covers all possible architectures we want to consider. If there are possible architectures , then the output of One-Shot net and DARTS is (as summarized in ProxylessNAS [8]):

, where in is a softmax distribution over the architectures. To be clear, from the equation above, in order to compute or , we have to compute all the architectures’ outputs.  

The problem with One-Shot and DARTS is that the memory needs to hold all architectures hence may easily blow up. ProxylessNAS proposes a technique called BinaryConnect, which is very close to DARTS but has subtle difference. BinaryConnect means that , where is sampled from a softmax distribution. The difference with DARTS is that is strictly one architecture’s output, rather than a weighted sum of architectures. To take gradients of , they propose a trick to sample two architectures every time when computing the gradient:

ProxylessNAS also proposes to train a neural network to predict latency so that model prediction accuracy and latency can be both differentiable w.r.t. architectures.

ENAS [12] is actually the originator of the weight sharing technique. One hurdle ENAS has over ProxylessNAS is that it requires an additional RNN controller to decide which architecture to sample. ProxylessNAS only needs to learn the softmax distribution parameters .

TuNAS [6] can be seen as an improved version over ProxylessNAS. There are mainly two improvements:

(1) more aggressive weight sharing, which they called operation collapsing.

(2) a new reward function, which they claim leads to more robust results:

In TuNAS, policy gradient is used for sampling potential architectures, while weight sharing updates the sampled architectures’ weights. As the RL policy samples more and more architectures which cover all possible weights, all the weights in the biggest architecture get learned well. The overall learning loop is described as:

then is a learnable vector determining which operator to be more preferable. Suppose the network’s own weight is , then the objective function of DARTS is essentially:
Note that is actually optimized on the validation dataset. As the paper suggests, this is a bi-level optimization problem. Analytically, the optimal solution is obtained when and .

The paper proposes to replace , the expensive minimization , with .

However, now and , the first and second argument in , are both a function of , so we need to use the derivative rule of multi-variable functions to really compute . I refer to https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/14%3A_Differentiation_of_Functions_of_Several_Variables/14.5%3A_The_Chain_Rule_for_Multivariable_Functions and https://www.programmersought.com/article/14295360685/#67_176 to really understand how to compute .

We use a simpler notation to represent , where , , .

From the derivative rule of multi-variable functions

we have:

So we finally compute as: 

       

As you may notice, is an expensive matrix-vector product, so people propose to use the finite difference approximation:

where  

The finite difference approximation is actually based on Taylor expansion:

The problem with DARTS is that after learning both the architecture selection parameter and the supernet’s own weight , it derives the best child network by . As pointed out by SNAS [14], DARTS thus has “the inconsistency between the performance of derived child networks and converged parent networks”. SNAS uses the concrete distribution as the more principled way to learn the architecture selection parameter . In the concrete distribution, there is a parameter that will be annealed to be close to zero thus when the training finished, the architecture selection parameter will converge to discrete variables (clearly denoting which operator is connected between which pair of nodes). 

The notations in the SNAS paper [14] is a bit chaotic. Hope I can comb them more cleanly. The idea of SNAS is that the architecture search parameter is a binary tensor . denotes the node is connected to node with operator . Therefore, is actually a one-hot encoding vector of length , i.e., the selection of one of the possible operators connecting node and . Similarly, is also a vector of length , denoting the output of the possible operators.

Therefore, the objective function of SNAS is:

   

where is the model’s own loss.

Now, will be parameterized by the concrete distribution, which constitutes the parameter selection parameter of the same size of , i.e., , the Gumbel random variable , and the annealing parameter . Specifically,

   

The authors proves that is essentially doing policy gradient.

First, we make sure we are clear on the notations on how node ‘s input interacts with other nodes that connect to it (small modification from equation 20 in [14]):

   

Now, using the chain rule of derivatives, we have

   

Finally, Appendix D shows that:

That’s the form of policy gradient. That’s why it is equivalent to say that SNAS is trained with policy gradient and with reward .

I’ll dig into DSNAS [15] once it gets more attention.

——————– Update 2021/09 ——————–

I want to mention two more classic ideas of NAS.

1. Regularized evolution [17], in which every mutated solution has a certain survival period. The only way that a good architecture can remain the population is by being passed down from parents to children through the generations. “regularized” means every solution has an age, therefore it encourages more diversity and exploration and avoids being stuck by spuriously promising solutions.
2. Bayesian Optimization [18], in which there are five most important components: encoding, neural predictor, uncertainty estimate, acquisition function, and acquisition optimization. [18] used empirical experiments to find the optimal combination of them: path encoding (a specific feature engineering method they propose), an ensemble of 5 feedforward neural networks as uncertainty estimate, independent Thompson Sampling, and mutation-based acquisition optimization.

 

References (arxiv submitted time)

[1] NEURAL ARCHITECTURE SEARCH WITH REINFORCEMENT LEARNING (2016.11)

[2] AutoML-Zero: Evolving Machine Learning Algorithms From Scratch (2020.3)

[3] EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks (2019.5)

[4] MnasNet: Platform-aware neural architecture search for mobile (2018.7)

[5] Neural Predictor for Neural Architecture Search (2019.12)

[6] Can weight sharing outperform random architecture search? An investigation with TuNAS (2020.8)

[7] BigNAS: Scaling Up Neural Architecture Search with Big Single-Stage Models (2020.3)

[8] ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware (2018.12)

[9] Progressive Neural Architecture Search (2017.12)

[10] Understanding and Simplifying One-Shot Architecture Search (2018)

[11] DARTS: Differentiable Architecture Search (2018. 6)

[12] Efficient Neural Architecture Search via Parameter Sharing (2018.2)

[13] Few-shot Neural Architecture Search (2020.6) 

[14] SNAS: Stochastic Neural Architecture Search (2018.12)

[15] DSNAS: Direct Neural Architecture Search without Parameter Retraining (2020.2)

[16] softmax derivative trick https://eli.thegreenplace.net/2016/the-softmax-function-and-its-derivative/

[17] Regularized Evolution for Image Classier Architecture Search (2019.2)

[18] BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search (2020.11)

I’ll introduce some recent papers advancing batch RL.

The first paper is Critic Regularized Regression [1]. It starts from a general form of actor-critic policy gradient objective function, where is a learned critic function:

For a behavior cloning method, . However, we can do much more than that choice:

The CRR paper tested the first two choices, while another famous algorithm Advantage Weighted Behavior Model (ABM) from paper (Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning) [2] used the third choice.

 

CRR can be connected to a popular family of policy gradient algorithms called Maximum a Posteriori Policy Optimisation (MPO) [3], which I think is better summarized in [2]. From [2], we can see that MPO solves problems in the following form:

The optimal solution by MPO has a closed form expression:

In CRR, is equal to the logging policy . So the optimal solution is supposed to be . The CRR paper points out it is equivalent to subtract the state value from , leading to . (I am not sure how is omitted. )

The overall learning loop of CRR is very straightforward:

 

Let’s look at how MPO is used in the ABM paper [2]. While in CRR is the logging policy , in ABM could also be a behavior cloning policy mimicking the logging policy or the advantaged-based behavior cloning policy.

As argued in [2], the reason to not simply using a behavior cloning prior is to avoid learning from a very mediocre logging policy:

Once we obtain , we can learn the RL policy using Eqn. 2. [2] provides two ways of optimization: (1) Expectation-Maximization, alternating between and the Lagrangian multiplier ; (2) stochastic gradient descent with reparameterization trick because there is in the objective.

 

The next paper is conservative Q-learning [4]. The idea is simple though the proof in the paper is too dense to understand. I am following https://towardsdatascience.com/the-power-of-offline-reinforcement-learning-5e3d3942421c to illustrate its idea. In standard Q-learning, our loss function is:

   

A very conservative Q-learning loss function is:

   

which can be understood intuitively as you are always dragging down the Q-values of whichever action selected by the learned policy.

However, the authors find in this way the Q values are learned too conservative. Therefore, they propose a relaxing version of loss:

   

This objective can be understood that we not only drag down the Q-values of the learned policy’s actions, but also pull up the Q-values of the logged actions. As a balance, the resultant Q-function is more conservative in actions not seen but less conservative in actions seen in the logged data.

 

Different batch RL can all be boiled down to how to extrapolate Q-values on unobserved/less observed (state, action) pairs. [5] provides a principled way to zero out those “uncertain” Q-values. Here are some basic notations for introducing their idea:

There are two paradigms of learning a policy from data: policy iteration and value iteration. [5]’s methodology can be plugged in either paradigm.

For policy iteration (they call MBS-PI):

For value iteration (they call MBS-QI):

You can see that their methods all come down a filter , which simply zeros out Q values of (state, action) frequency less than a threshold:

It is interesting to see how we empirically compute , the count/probability distribution of encountering (state, action) pairs.

• For discrete action problems, they discretize state spaces by binning each state feature dimension. Therefore, there are a finite number of (state, action) pairs for which they count frequencies.
• For continuous action problems, we can train a VAE to learn , the lower bound of , as the objective function. Once the VAE is learned, we can compute by , where is an indicator function. 
• For continuous action problems, another methodology, which is used in the paper, is to integrate with BCQ [7]. BCQ trains a conditional VAE to only sample actions similar to the data collection policy in Bellman update. One drawback of BCQ is that it only considers sampling likely actions, even if the state is less observed. In comparison, [5] takes into consider the observation frequency of both states and actions. Since BCQ already prevents Q-values from backing-up on low frequent actions (given any state), they only need to apply on BCQ-updated Q-values to further zero out Q-values with less observed states. comes from a VAE trained only on state data.

Let’s recap how VAE works, mainly based on my previous post: Stochastic Variational Inference, Optimization with discrete random variables, and a nice online post https://wiseodd.github.io/techblog/2016/12/17/conditional-vae/. Suppose a VAE contains an encoder (encoding input to a latent vector ) and a generator (reconstructing the input based on ). and entail the probability density of the latent vector and the reconstructed input. Usually, , where and are the output of the encoder. VAE optimizes an objective function called ELBO (Evidence Lower Bound):

.

Now, if you just let your VAE learn on states (as ) collected by a behavior policy , then once this VAE is learned, you can compute ELBO for any test state , which can be interpreted as the lower bound of how likely would appear under the same behavior policy .  

A conditional VAE [6] only requires small modifications to normal VAEs, where denotes a condition vector:

In real implementation, we just need to concatenate to the latent vector and the input and keep the rest of VAE training code unchanged.

 

As I said, different batch RL can all be boiled down to how to extrapolate Q-values on unobserved/less observed (state, action) pairs. BEAR from [8] is another example. While BCQ, MBS-PI, and MBS-QI have implicit constraints on being close to the behavior policy (i.e., prevent Q-value back-ups on less observed state/action pairs), BEAR has a more explicit constraint in its objective function:

where MMD is maximum mean discrepancy measuring the distance between two distributions using empirical samples:

MMD is illustrated very well in this post: https://stats.stackexchange.com/questions/276497/maximum-mean-discrepancy-distance-distribution. And it is also used in InfoVAE to replace the KL divergence term in the loss function of traditional VAE (recall that the ELBO objective consists of two terms, reconstruction error and KL divergence to encourage the latent vector to be close to the prior). As argued in https://ermongroup.github.io/blog/a-tutorial-on-mmd-variational-autoencoders/, KL divergence may push and to be close for every input, which may result to a VAE ended up with learning a uninformative latent code, while MMD-based VAE only encourages and to be close in expectation. 

Overall, the algorithm’s pseudocode works as below:

  

References

[1] Critic Regularized Regression: https://arxiv.org/abs/2006.15134

[2] Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning: https://arxiv.org/abs/2002.08396

[3] Maximum a Posteriori Policy Optimisation (https://arxiv.org/abs/1806.06920)

[4] Conservative Q-Learning for Offline Reinforcement Learning: https://arxiv.org/abs/2006.04779

[5] Provably Good Batch Reinforcement Learning Without Great Exploration: https://arxiv.org/abs/2007.08202

[6] Conditional Generative Adversarial Nets: https://arxiv.org/abs/1411.1784. Nice post: https://wiseodd.github.io/techblog/2016/12/17/conditional-vae/

[7] Off-Policy Deep Reinforcement Learning without Exploration: https://arxiv.org/abs/1812.02900

[8] Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction: https://arxiv.org/abs/1906.00949

I am reading two papers which uses very classical methodologies for optimizing metrics in real world applications.

The first is constrained optimization for ranking, from The NodeHopper: Enabling Low Latency Ranking with Constraints via a Fast Dual Solver. The paper performs per-slate constrained optimization:

Here, is item ‘s primary metric value, is item ‘s position after ranking , and means the attention strength on each item when the item is ranked by . Similarly, is the constraint matrix. As you can see, they define the slate reward/constraint as the sum of per-item rewards/constraints, which may or may not be the case for some application. 

If there are items, there will be possible rankings. Therefore, optimizing Eqn. 1 will be hard. They skillfully convert the problem into something more manageable. First, they rewrite Eqn. 1 into Eqn. 2:

is a permutation matrix (each row and column has exactly one 1). 

Then, they relax to be a probabilistic matrix, , an “expected” permutation matrix. (In 3d, there is a typo. It should be ). Here, is a distribution for all possible permutations.

Now, we can just optimize w.r.t. , which has only entries:

Finally, Eqn. 4 can be solved by the Lagrangian method

The rest of the paper is really complicated and hard to understand. But they are solving the same constrained optimization problem.

The second paper I read is named “Automated Creative Optimization for E-Commerce Advertising” (https://arxiv.org/abs/2103.00436). The background of this paper is that in online advertising, each candidate ads contain a set of interactive elements as a combination, such as templates, fonts, and backgrounds.

An ad’s CTR can be naturally predicted using Factorization Machine (from Eqn.3. in the paper): 

The explanation for Eqn. 3 is that, there are elements in an ads . and are the embeddings of a pair of elements, where the interaction score between the two embeddings could be computed using one of the operators, Concat, Multiply, Plus, Max, or Min. (mentioned in Section 4.2).

The problem the paper tries to solve is that when the system has many ads candidates, how can the system pick the best ads candidate believed to have the highest CTR while balancing the need to explore the element space? So they use Thompson Sampling with Bayesian Contextual Bandit. The bayesian part comes from that all embeddings (, , …) are bayesian estimates from a Gaussian distribution. For every next ads, they sample embedding values from the present distribution, pick the best ads, observe the reward, and then update the posterior distribution. 

How do we update the embedding estimates ? We use stochastic variational inference (https://czxttkl.com/2019/05/04/stochastic-variational-inference/). We can optimize with gradient-based methods w.r.t. the ELBO function, which contains only a likelihood (given a sampled , how likely is to observe the current dataset?) and a KL divergence between the current Gaussian distribution and a prior Gaussian distribution, both of which have an analytical expression. 

This paper is a classical example of stochastic variational inference and could be applied to many real-world problems. 

In reinforcement learning (RL), it is common that a task only reveals rewards sparsely, e.g., at the end of an episode. This prevents RL algorithms from learning efficiently, especially when the task horizon is long. There has been some research on how to distribute sparse rewards to more preceding steps.

One simple, interesting research is [1]. Its loss is defined as:
The loss can be understood as that each step’s reward constitutes contribution from the current state and all previous states , gated by .

[7] uses Transformers (or any attention-based sequence models) to decompose episode reward to step rewards. The loss function is:
You can think of in the subscript of and as , i.e., the Transformers will take into accounts all previous steps until the current step to make the prediction of reward for the current step. The difference with [1] is that: a. [7] uses previous steps’ information more effectively using a sequence model; b. [7] only decomposes the total episode reward , while [1] decomposes for every step reward.

Another research is Hindsight Experience Replay (HER) [4], in which we create spurious but easier-to-achieve rewards. This repository has a clear implementation [5]. 

HER is best explained using an example, a bit-flipping environment, as described below:
As you can see, this environment could have states and only one state could give you a positive reward. It would almost be infeasible for a normal RL model to explore and learn effectively. What confused me but now is clear to me is that the state of this environment fed to an RL model has two parts, the current bits and the target bits. This is manifested in the agent’s learn function in [5].

The crux of HER is as follows. Even when an episode terminates and fails, we augment the replay buffer with some new tuples, pretending that we want to arrive the last state as the target goal.

Because of these intermediate easier goals being attached to the state, the RL model has more non-sparse experience to learn from to reach the goal specified in its state.

Finally, there is work called Temporal Value Transport [8], with a blog [9] explaining it. I think this work is very heuristic-driven. Suppose one episode has steps, they use a sequence model with attention mechanism to predict each pair of steps ‘s influence on reward (). Specifically, the sequence model is a classifier predicting whether “the logit predicting whether the rewards-to-go from a given observation are below or above a threshold.” (from [9]). 

 

 

 

 

 

Then, the reward is re-distributed by:

 

Below is two works that I do not understand fully.

The first is [6]. It converts the normal policy gradient update:

to:

where contains the future part of the trajectory after time step . The intuition that in off-policy learning, we can utilize the steps after the current step to make better value estimation. However, I do not understand how is computed (the paper says it is from a classifier based on RNN) and what represents.

The second is RUDDER [2], with its web-view blog explaining it [3]. However, I still do not get it how LSTM is used in RUDDER to distribute rewards. [1]’s related work sheds some lights on how RUDDER works, though:

 

References

[1] Synthetic Returns for Long-Term Credit Assignment: https://arxiv.org/pdf/2102.12425.pdf

[2] RUDDER: Return Decomposition for Delayed Rewards https://arxiv.org/pdf/1806.07857.pdf

[3] https://ml-jku.github.io/rudder/

[4] Hindsight Experience Replay: https://arxiv.org/pdf/1707.01495.pdf

[5] https://github.com/hemilpanchiwala/Hindsight-Experience-Replay

[6] COUNTERFACTUAL CREDIT ASSIGNMENT IN MODEL-FREE REINFORCEMENT LEARNING: https://arxiv.org/pdf/2011.09464.pdf

[7] Sequence modeling of temporal credit assignment for episodic reinforcement learning: https://arxiv.org/pdf/1905.13420.pdf

[8] Optimizing agent behavior over long time scales by transporting value: https://www.nature.com/articles/s41467-019-13073-w.pdf

[9] https://www.efavdb.com/ltca

I am reading some self-supervised learning papers. Some of them have interesting tricks to create self-supervised learning signals. This post is dedicated for those tricks.

The first paper I read is SwAV(Swapping Assignments between multiple Views of the same image) [1]. The high level idea is that we create clusters with cluster centers . These cluster centers are trainable parameters. More importantly, these cluster centers will be used in every training batch. In each batch, we distort (augment) each image into two versions. For each version, the distorted images are transformed to an embedding space and clustered equally by the clusters. As you might guess, the two distorted images from the same original image should belong to the same cluster.

The clustering-based method has an advantage over contrastive learning directly on image features because the former operates on a smaller input space when doing pairwise comparisons:

The interesting trick in SwAV is to partition images equally to the clusters. If we denote to be the image-cluster center similarity matrix, then the problem is converted to finding such that:

The constraints enforce that on average each cluster is associated with data points. As illustrated in [1], they find the continuous code using the iterative Sinkhorn-Knopp algorithm.

SwAV has been used to train on 1 billion random instagram images. The resulting models (called SEER) achieve SOTA top1 accuracy on ImageNet data after fine tuning. [2]

References

[1] Unsupervised Learning of Visual Features by Contrasting Cluster Assignments: https://arxiv.org/pdf/2006.09882.pdf 

[2] Self-supervised Pretraining of Visual Features in the Wild: https://arxiv.org/abs/2103.01988