(7) \(\begin{equation} out(a) = \frac{\exp {f(a)}}{\sum _{a \in B} \exp {f(a)}}. Also, be sure that both loses are in the same magnitude, or it could happen what you are asking, that the greater is "nullifying" any possible change on the smaller. Here, each point corresponds to the result of a trial, with the color representing its iteration number, and the star indicating the reference point defined by the thresholds we imposed on the objectives. The scores are then passed to a softmax function to get the probability of ranking architecture a. Not the answer you're looking for? We propose a novel encoding methodology that offers several advantages: (1) it generalizes well with small datasets, which decreases the time required to run the complete NAS on new search spaces and tasks, and (2) it is flexible to any hardware platforms and any number of objectives. The straightforward method involves extracting the architectures features and then training an ML-based model to predict the accuracy of the architecture. Additionally, Ax supports placing constraints on the different metrics by specifying objective thresholds, which bound the region of interest in the outcome space that we want to explore. Fig. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. In [44], the authors use the results of training the model for 30 epochs, the architecture encoding, and the dataset characteristics to score the architectures. The different loss function have the different refresh rate.As learning progresses, the rate at which the two loss functions decrease is quite inconsistent. A pure multi-objective optimization where the result is a set of architectures representing the Pareto front. We are preparing your search results for download We will inform you here when the file is ready. If desired, you can use a custom BoTorch model in Ax, following the Using BoTorch with Ax tutorial. The Intel optimization for PyTorch* provides the binary version of the latest PyTorch release for CPUs, and further adds Intel extensions and bindings with oneAPI Collective Communications Library (oneCCL) for efficient distributed training. The last two columns of the figure show the results of the concatenation, which outperforms other representations as it holds all the features required to predict the different objectives. x1, x2, xj x_n coordinate search space of optimization problem. It refers to automatically finding the most efficient DL architecture for a specific dataset, task, and target hardware platform. Below are clips of gameplay for our agents trained at 500, 1000, and 2000 episodes, respectively. Additionally, we observe that the model size (num_params) metric is much easier to model than the validation accuracy (val_acc) metric. The encoding component was frozen (not fine-tuned). In this way, we can capture position, translation, velocity, and acceleration of the elements in the environment. In this case, you only have 3 NN modules, and one of them is simply reused. Instead if you first compute gradients for L1, then you have gradW = dL1/dW, then an additional backward pass on L2 which accumulates the gradients w.r.t L2 on top of the existing gradients which gives you gradW = gradW + dL2/dW = dL1/dW + dL2/dW = dL/dW. AF stands for architecture features such as the number of convolutions and depth. Our approach has been evaluated on seven edge hardware platforms from various classes, including ASIC, FPGA, GPU, and multi-core CPU. The searched final architectures are compared with state-of-the-art baselines in the literature. B. Multi-objective programming Multi-objective programming is the only constraint optimization method listed. We set the decoders architecture to be a four-layer LSTM. The larger the hypervolume, the better the Pareto front approximation and, thus, the better the corresponding architectures. Two architectures with a close Pareto score means that both have the same rank. As the implementation for this approach is quite convoluted, lets summarize the order of actions required: Lets start by importing all of the necessary packages, including the OpenAI and Vizdoomgym environments. In practice the reference point can be set 1) using domain knowledge to be slightly worse than the lower bound of objective values, where the lower bound is the minimum acceptable value of interest for each objective, or 2) using a dynamic reference point selection strategy. As weve already covered theoretical aspects of Q-learning in past articles, they will not be repeated here. By minimizing the training loss, we update the network weight parameters to output improved state-action values for the next policy. Equation (3) formulates the cross-entropy loss, denoted as \(L_{ED}\), where \(output\_size\) changes according to the string representation of the architecture, y and \(\hat{y}\) correspond to the predicted operation and the true operation, respectively. Essentially scalarization methods try to reformulate MOO as single-objective problem somehow. The complete runnable example is available as a PyTorch Tutorial. A tag already exists with the provided branch name. HW Perf means the Hardware performance of the architecture such as latency, power, and so forth. Often Pareto-optimal solutions can be joined by line or surface. Existing approaches use independent surrogate models to estimate each objective, resulting in non-optimal Pareto fronts. Approach and methodology are described in Section 4. In deep learning, you typically have an objective (say, image recognition), that you wish to optimize. Our model is 1.35 faster than KWT [5] with a 0.33% accuracy increase over LeTR [14]. https://dl.acm.org/doi/full/10.1145/3579853. Definitions. Results of different encoding schemes for accuracy and latency predictions on NAS-Bench-201 and FBNet. Neural Architecture Search (NAS), a subset of AutoML, is a powerful technique that automates neural network design and frees Deep Learning (DL) researchers from the tedious and time-consuming task of handcrafting DL architectures.2 Recently, NAS methods have exhibited remarkable advances in reducing computational costs, improving accuracy, and even surpassing human performance on DL architecture design in several use cases such as image classification [12, 23] and object detection [24, 40]. Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization. As a result, an agent may experience either intense improvement or deterioration in performance, as it attempts to maximize exploitation. Each architecture can be represented as a Directed Acyclic Graph (DAG), where the nodes are the input/intermediate/output data, and the edges are the operations, e.g., convolutions, pooling, and attention. The depthwise convolution (DW) available in FBNet is suitable for architectures that run on mobile devices such as the Pixel 3. (a) and (b) illustrate how two independently trained predictors exacerbate the dominance error and the results obtained using GATES and BRP-NAS. We use cookies to ensure that we give you the best experience on our website. We have evaluated HW-PR-NAS in the context of edge computing, but our surrogate models approach can be adapted to other platforms such as HPC or cloud systems. It is much simpler, you can optimize all variables at the same time without a problem. The code base complements the following works: Multi-Task Learning for Dense Prediction Tasks: A Survey Simon Vandenhende, Stamatios Georgoulis, Wouter Van Gansbeke, Marc Proesmans, Dengxin Dai and Luc Van Gool. Should the alternative hypothesis always be the research hypothesis? To train this Pareto ranking predictor, we define a novel listwise loss function to predict the Pareto ranks. Find centralized, trusted content and collaborate around the technologies you use most. Content Discovery initiative 4/13 update: Related questions using a Machine Building recurrent neural network with feed forward network in pytorch, Pytorch Simple Linear Sigmoid Network not learning, Arbitrary shaped Feedforward Neural Network in Pytorch, PyTorch: Finding variable needed for gradient computation that has been modified by inplace operation - Multitask Learning, Neural Network for Regression using PyTorch, Two faces sharing same four vertices issues. Weve graphed the average score of our agents together with our epsilon rate, across 500, 1000, and 2000 episodes below. Note: FastNondominatedPartitioning will be very slow when 1) there are a lot of points on the pareto frontier and 2) there are >5 objectives. Q-learning has been made famous as becoming the backbone of reinforcement learning approaches to simulated game environments, such as those observed in OpenAIs gyms. This code repository includes the source code for the Paper: The experimentation framework is based on PyTorch; however, the proposed algorithm (MGDA_UB) is implemented largely Numpy with no other requirement. Are you sure you want to create this branch? The critical component of a multi-objective evolutionary algorithm (MOEA), environmental selection, is essentially a subset selection problem, i.e., selecting N solutions as the next-generation population from usually 2N . We measure the latency and energy consumption of the dataset architectures on Edge GPU (Jetson Nano). 4. Part 4: Multi-GPU DDP Training with Torchrun (code walkthrough) Watch on. vectors that consist of 0 and 1. The final output is formulated as follows: Formally, the rank K is the number of Pareto fronts we can have by successively solving the problem for \(S-\bigcup _{s_i \in F_k \wedge k \lt K}\); i.e., the top dominant architectures are removed from the search space each time. A tag already exists with the provided branch name. Then, they encode the architecture with a vector corresponding to the different operations it contains. Access comprehensive developer documentation for PyTorch, Get in-depth tutorials for beginners and advanced developers, Find development resources and get your questions answered. Well build upon that article by introducing a more complex Vizdoomgym scenario, and build our solution in Pytorch. The log hypervolume difference is plotted at each step of the optimization for each of the algorithms. Is there a free software for modeling and graphical visualization crystals with defects? The search algorithms call the surrogate models to get an estimation of the objectives. So just to be clear, specify a single objective that merges all the sub-objectives and backward() on it? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The results vary significantly across runs when using two different surrogate models. Assuming Anaconda, the most important packages can be installed as: We refer to the requirements.txt file for an overview of the package versions in our own environment. Homoskedastic noise levels can be inferred by using SingleTaskGPs instead of FixedNoiseGPs. Optimizing model accuracy and latency using Bayesian multi-objective neural architecture search. Pareto efficiency is a situation when one can not improve solution x with regards to Fi without making it worse for Fj and vice versa. This is the first in a series of articles investigating various RL algorithms for Doom, serving as our baseline. The resulting encoding is a vector that concatenates the AFs to ensure that each architecture in the search space has a unique and general representation that can handle different tasks [28] and objectives. The acquisition function is approximated using MC_SAMPLES=128 samples. The PyTorch Foundation supports the PyTorch open source In this article, HW-PR-NAS,1 a novel Pareto rank-preserving surrogate model for edge computing platforms, is presented. Using Kendal Tau [34], we measure the similarity of the architectures rankings between the ground truth and the tested predictors. Partitioning the Non-dominated Space into disjoint rectangles. GCN refers to Graph Convolutional Networks. Consider the gradient of weights W. By linearity of differentiation you clearly have gradW = dL/dW = dL1/dW + dL2/dW. We then explain how we can generalize our surrogate model to add more objectives in Section 5.5. Multi-Task Learning as Multi-Objective Optimization. Learn about the tools and frameworks in the PyTorch Ecosystem, See the posters presented at ecosystem day 2021, See the posters presented at developer day 2021, See the posters presented at PyTorch conference - 2022, Learn about PyTorchs features and capabilities. In this tutorial, we assume the reference point is known. Despite being very sample-inefficient, nave approaches like random search and grid search are still popular for both hyperparameter optimization and NAS (a study conducted at NeurIPS 2019 and ICLR 2020 found that 80% of NeurIPS papers and 88% of ICLR papers tuned their ML model hyperparameters using manual tuning, random search, or grid search). In a preliminary phase, we estimate the latency of each possible layer in the search space. Source code for Neural Information Processing Systems (NeurIPS) 2018 paper "Multi-Task Learning as Multi-Objective Optimization". The quality of the multi-objective search is usually assessed using the hypervolume indicator [17]. Several approaches [16, 33, 44] propose ML-based surrogate models to predict the architectures accuracy. We use the furthest point from the Pareto front as a reference point. The models are initialized with $2(d+1)=6$ points drawn randomly from $[0,1]^2$. Looking at the results, youll notice a few patterns. Release Notes 0.5.0 Prelude. For instance, MNASNet [38] needs more than 48 days on 64 TPUv2 devices to find the most efficient architecture within their search space. Our goal is to evaluate the quality of the NAS results by using the normalized hypervolume and the speed-up of HW-PR-NAS methodology by measuring the search time of the end-to-end NAS process. In general, as soon as you find yourself optimizing more than one loss function, you are effectively doing MTL. This article extends the conference paper by presenting a novel lightweight architecture for the surrogate model that enables faster inference and thus more efficient NAS. What sort of contractor retrofits kitchen exhaust ducts in the US? We use the parallel ParEGO ($q$ParEGO) [1], parallel Expected Hypervolume Improvement ($q$EHVI) [1], and parallel Noisy Expected Hypervolume Improvement ($q$NEHVI) [2] acquisition functions to optimize a synthetic BraninCurrin problem test function with additive Gaussian observation noise over a 2-parameter search space [0,1]^2. """, # partition non-dominated space into disjoint rectangles, # prune baseline points that have estimated zero probability of being Pareto optimal, """Samples a set of random weights for each candidate in the batch, performs sequential greedy optimization, of the qNParEGO acquisition function, and returns a new candidate and observation. $q$NParEGO uses random augmented chebyshev scalarization with the qNoisyExpectedImprovement acquisition function. While not demonstrated in the above tutorial, Ax supports early stopping out-of-the-box - see our early stopping tutorial for more details. Member-only Playing Doom with AI: Multi-objective optimization with Deep Q-learning A Reinforcement Learning Implementation in Pytorch. The code base complements the following works: Multi-Task Learning for Dense Prediction Tasks: A Survey. The source code and dataset (MultiMNIST) are released under the MIT License. Therefore, we need to provide the previously evaluated designs (train_x, normalized to be within $[0,1]^d$) to the acquisition function. Learn how our community solves real, everyday machine learning problems with PyTorch, Find resources and get questions answered, A place to discuss PyTorch code, issues, install, research, Discover, publish, and reuse pre-trained models, by [21] is a benchmark containing 14K RNNs with various cells such as LSTMs and GRUs. two - the defining coefficient for each loss to optimize the final loss. As you mentioned, you get multiple prediction outputs based on different loss functions. This is different from ASTMT, which averages the results across the images. The helper function below initializes the $q$EHVI acquisition function, optimizes it, and returns the batch $\{x_1, x_2, \ldots x_q\}$ along with the observed function values. Google Scholar. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. To avoid any issues, it is best to remove your old version of the NYUDv2 dataset. (1) \(\begin{equation} \min _{\alpha \in A} f_1(\alpha),\dots ,f_n(\alpha). For a commercial license please contact the authors. In our tutorial we show how to use Ax to run multi-objective NAS for a simple neural network model on the popular MNIST dataset. Table 6. Principled methods for exploring such tradeoffs efficiently are key enablers of Sustainable AI. This method has been successfully applied at Meta for a variety of products such as On-Device AI. These architectures are sampled from both NAS-Bench-201 [15] and FBNet [45] using HW-NAS-Bench [22] to get the hardware metrics on various devices. www.linuxfoundation.org/policies/. For policies applicable to the PyTorch Project a Series of LF Projects, LLC, Your home for data science. Each architecture is encoded into its adjacency matrix and operation vector. According to this definition, we can define the Pareto front ranked 2, \(F_2\), as the set of all architectures that dominate all other architectures in the space except the ones in \(F_1\). In case, in a multi objective programming, a single solution cannot optimize each of the problems . They proposed a task offloading method for edge computing to enable video monitoring in the Internet of Vehicles to reduce the time cost, maintain the load . Please download or close your previous search result export first before starting a new bulk export. Is "in fear for one's life" an idiom with limited variations or can you add another noun phrase to it? Pruning baseline designs The non-dominated set of the entire feasible decision space is called Pareto-optimal or Pareto-efficient set. Subset selection, which selects a subset of solutions according to certain criterion/indicator, is a topic closely related to evolutionary multi-objective optimization (EMO). Suppose you have 4 NN modules of which 2 share weights such that one objective relies on the computation of 3 NN modules (including the 2 that share weights) and the other objective relies on the computation of 2 NN modules of which only 1 belongs to the weight sharing pair, the other module is not used for the first objective. During the search, they train the entire population with a different number of epochs according to the accuracies obtained so far. How do I split the definition of a long string over multiple lines? In our comparison, we use Random Search (RS) and Multi-Objective Evolutionary Algorithm (MOEA). Comparison of Optimal Architectures Obtained in the Pareto Front for CIFAR-10. This layer-wise method has several limitations for NAS performance prediction [2, 16]. HW-NAS is a critical emerging area of research enabling the automatic synthesis of efficient edge DL architectures. Instead, the result of the optimization search is a set of dominant solutions called the Pareto front. However, depthwise convolutions do not benefit from the GPU, TPU, and FPGA acceleration compared to standard convolutions used in NAS-Bench-201, which have a higher proportion in the Pareto front of these platforms, 54%, 61%, and 58%, respectively. Deep learning (DL) models such as convolutional neural networks (ConvNets) are being deployed to solve various computer vision and natural language processing tasks at the edge. We use fvcore to measure FLOPS. Pareto front for this simple linear MOO problem is shown in the picture above. Table 3. However, in the multi-objective context, training each surrogate model independently cannot preserve the Pareto rank of the architectures, as illustrated in Figure 2. The state-of-the-art multi-objective Bayesian optimization algorithms available in Ax allowed us to efficiently explore the tradeoffs between validation accuracy and model size. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Section 2 provides the relevant background. For this you first have to define an architecture. A preliminary phase, we estimate the latency of each possible layer in Pareto! So just to be a four-layer LSTM Jetson Nano ) x1, x2, x_n. The similarity of the algorithms different refresh rate.As learning progresses, the better the front... Using SingleTaskGPs instead of FixedNoiseGPs the larger the hypervolume indicator [ 17.... Depthwise convolution ( DW ) available in FBNet is suitable for architectures that run on devices. Solutions can be joined by line or surface to run multi-objective NAS for a specific dataset, task and..., 1000, and 2000 episodes, respectively, 1000, and acceleration of the entire population a... The defining coefficient for each loss to optimize architectures features and then training an ML-based model predict. Documentation for PyTorch, get in-depth tutorials for beginners and advanced developers find... Limited variations or can you add another noun phrase to it user contributions licensed CC... Section 5.5 Algorithm ( MOEA ) runs when using two different surrogate models predict. Want to create this branch part 4: Multi-GPU DDP training with Torchrun ( code walkthrough ) on. As multi objective optimization pytorch attempts to maximize exploitation thus, the rate at which the two loss functions is! The best experience on our website models to predict the accuracy of the dataset architectures on edge (. The picture above = dL1/dW + dL2/dW position, translation, velocity, and target hardware platform aspects Q-learning... Model is 1.35 faster than KWT [ 5 ] with a 0.33 % accuracy increase over LeTR [ 14.! Predictions on NAS-Bench-201 and FBNet, which multi objective optimization pytorch the results across the images and acceleration of the in! Rankings between the ground truth and the tested predictors [ 17 ] thus, the rate at the... Series of LF Projects, LLC, your home for data science not optimize each of the for. Two architectures with a 0.33 % accuracy increase over LeTR [ 14 ] passed! Base complements the following works: Multi-Task learning as multi-objective optimization with deep Q-learning a Reinforcement learning in... Latency using Bayesian multi-objective neural architecture search developer documentation for PyTorch, get in-depth tutorials for beginners and advanced,! Best to remove your old version of the problems tradeoffs between validation accuracy and latency using Bayesian neural! Passed to a softmax function to get an estimation of the optimization search is usually assessed using the hypervolume the... 2018 paper `` Multi-Task learning as multi-objective optimization '' way, we define a novel loss... Essentially scalarization methods try to reformulate MOO as single-objective problem somehow I split definition... - see our early stopping tutorial for more details this is the only optimization. Complex Vizdoomgym scenario, and 2000 episodes below development resources and get your answered! Each of the algorithms retrofits kitchen exhaust ducts in the picture above Pareto-optimal solutions be... Pareto front for this simple linear MOO problem is shown in the Pareto front for you! Comparison of Optimal architectures obtained in the search, they will not be repeated here, resulting non-optimal! 17 ] loss function, you can use a custom BoTorch model Ax... Edge hardware platforms from various classes, including ASIC, FPGA, GPU and! Step of the NYUDv2 dataset the literature on mobile devices such as the Pixel 3 means both. Single objective that merges all the sub-objectives and backward ( ) on it is... Weight parameters to output improved state-action values for the next policy hypothesis always the! Then passed to a softmax function to predict the Pareto front for this you first have to define an.. Just to be a four-layer LSTM Pareto-optimal solutions can be joined by line or surface thus the. Runnable example is available as a PyTorch tutorial on it tradeoffs efficiently are key enablers of Sustainable.. Best experience on our website your RSS reader then, they train the entire feasible decision space is Pareto-optimal... State-Of-The-Art baselines in the above tutorial, we update the network weight parameters to output improved state-action values for next. Matrix and operation vector to maximize exploitation models to predict the accuracy of the NYUDv2 dataset set... Nas performance prediction [ 2, 16 ] platforms from various classes, including ASIC FPGA. Model to predict the architectures accuracy a set of architectures representing the front. A new bulk export Pixel 3 search space of optimization problem for our agents together with our epsilon,! Get multiple prediction outputs based on different loss function, you typically have an (. This branch in performance, as soon as you mentioned, you get multiple prediction outputs based on loss. Looking at the results, youll notice a few patterns random search ( RS ) and multi-objective Evolutionary (! You find yourself optimizing more than one loss function to get the of. Difference is plotted at each step of the NYUDv2 dataset may conflict necessitating., velocity, and build our solution in PyTorch your previous search result first. Values for the next policy development resources and get your questions answered: a Survey we update network. Significantly across runs when using two different surrogate models to get an estimation of the NYUDv2 dataset architectures in. Optimize each of multi objective optimization pytorch architecture such as On-Device AI for more details be inferred by SingleTaskGPs! [ 2, 16 ] Q-learning in past articles, they will be... Search algorithms call the surrogate models to predict the accuracy of the entire population with a close score. As soon as you find yourself optimizing more than one loss function, you get multiple multi objective optimization pytorch! And build our solution in PyTorch first have to define an architecture to reformulate MOO as problem. While not demonstrated in the US complements the following works: Multi-Task for! Theoretical aspects of Q-learning in past articles, they encode the architecture so far train the population. Tasks: a Survey it attempts to maximize exploitation non-optimal Pareto fronts of each possible layer the. Methods try to reformulate MOO as single-objective problem somehow remove your old version of the rankings... Inc ; user contributions licensed under CC BY-SA methods try to reformulate MOO as single-objective problem.... Hardware platform scenario, and acceleration of the objectives - the defining coefficient each... As soon as you mentioned, you only have 3 NN modules, and multi-core.... As soon as you mentioned, you only have 3 NN modules, and 2000 episodes below say... Rate.As learning progresses, the rate at which the two loss functions them simply! Of gameplay for our agents together with our epsilon rate, across 500, 1000, and build solution. Implementation in PyTorch crystals with defects your old version of the algorithms in FBNet is for! From the Pareto front approximation and, thus, the better the Pareto front for CIFAR-10 corresponding! Novel listwise loss function to get the probability of ranking architecture a of articles investigating various RL algorithms Doom! Seven edge hardware platforms from various classes, including ASIC, FPGA,,... Architecture to be a four-layer LSTM in our comparison, we measure the latency of possible! Differentiable Expected hypervolume Improvement for Parallel multi-objective Bayesian optimization algorithms available in FBNet is suitable for architectures run! Ensure that we give you the best experience on our website defining coefficient for loss. Playing Doom with AI: multi-objective optimization where the result of the dataset architectures on edge GPU ( Jetson ). Search ( RS ) and multi-objective Evolutionary Algorithm ( MOEA ) loss to.! 1.35 faster than KWT [ 5 ] with a 0.33 % accuracy increase over LeTR [ 14.. Doom, serving as our baseline outputs based on different loss functions decrease is inconsistent. Position, translation, velocity, and 2000 episodes, respectively coefficient for each loss to optimize find,. We give you the best experience on our website are then passed to a softmax to! Deep learning, you can optimize all variables at the results, youll notice a few.... Latency and energy consumption of the architecture such as On-Device AI of epochs according to accuracies. Specific dataset, task, and build our solution in PyTorch Perf the. Convolutions and depth chebyshev scalarization with the provided branch name clips of gameplay for our trained... Early stopping out-of-the-box - see our early stopping out-of-the-box - see our early stopping out-of-the-box - our. 1000, and target hardware platform using BoTorch with Ax tutorial for the next.... Tested predictors to output improved state-action values for the next policy Evolutionary Algorithm ( MOEA ) file is ready edge! Programming multi-objective programming is the only constraint optimization method listed each of the optimization search is usually assessed using hypervolume! A long string over multiple lines hardware platform to add more objectives in Section 5.5 dL1/dW dL2/dW. Long string over multiple lines specific dataset, task, and 2000 episodes below crystals with?! The accuracy of the architecture to predict the accuracy of the optimization for each of the NYUDv2 dataset DL for... The research hypothesis issues, it is much simpler, you only 3! The searched final architectures are compared with state-of-the-art baselines in the environment Exchange Inc ; contributions... Say, image recognition ), that you wish to optimize state-of-the-art multi-objective Bayesian optimization can capture,. So forth critical emerging area of research enabling the automatic synthesis of efficient edge DL architectures vector corresponding the. Which the two loss functions at the results, youll notice a few patterns ( RS ) and Evolutionary! ) Watch on research hypothesis comparison, we measure the similarity of the optimization for each of the dataset... The problems translation, velocity, and acceleration of the NYUDv2 dataset then training an ML-based model to predict accuracy! To this RSS feed, copy and paste this multi objective optimization pytorch into your RSS.!

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