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Jacobian Descent for Multi-Objective Optimization

Quinton, Pierre, Rey, Valérian

arXiv.org Artificial Intelligence

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.


Here's why Machine Learning is the way to get ahead of your peers

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Online education in India is unfortunately underrated. Especially when it is touted as the future of education in our country. India's online education market is set to grow to $1.96 billion and almost 9.6 million users by 2021 from $247 million and around 1.6 million users in 2016. This year, it is believed that big data, machine learning, and data science will drive some of the top job opportunities in the country. There has already been a rapid advancement in the digital space that has led to a surge in demand for professionals skilled in the above-mentioned fields.


Give your career an 'UpGrad' and switch to a career in Machine Learning & AI

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The way we look at learning and education has been changing in recent times. Newer subjects like artificial intelligence are gaining more popularity as technology evolves at a rapid pace. However, getting the first-hand experience and understanding these newly developing subjects becomes extremely difficult for professionals. Machine learning and artificial intelligence are enablers that increase our productivity, but what is the best way to learn these new and evolving topics? UpGrad's PG program in Machine Learning and Artificial Intelligence in collaboration with IIIT-Bangalore has been ranked No 1 by Analytics India Magazine.


With 80% salary hikes, Machine Learning and AI is the hottest career right now

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When Argho Chatterjee decided to pursue UpGrad and IIIT Bangalore's PG Program in Machine Learning and Artificial Intelligence, he knew he was diving straight into coding his own artificial neural networks, and had a fair idea that this technology could help him solve real-world problems. What came as a pleasant surprise was that he had the access to a personalised learning environment provided by the prestigious institute through its partnership with distinguished online education venture – UpGrad. The two institutes have been working seamlessly to provide learners with an advanced curriculum, projects created in collaboration with the industry experts, and tailor-made support for AI career choices. In fact, the acclaimed degree went on to help Argho make a transition to the role of a Data Scientist ( Deep Learning (AI)) at Samsung R&D with 80% CTC hike! Learning in a personalised environment under great faculty, Argho brushed up on the basics, imbibed conceptual knowledge, and acquired full-fledged knowledge of the field.


UpGrad bets on AI for job creations, after Cambridge now partners with IIIT-B

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Few weeks after announcing a partnership with Cambridge Judge Business School, and earmarking Rs 200 crore for foraying into Southeast Asian Markets and the Middle East, UpGrad, the online higher education platform, has now announced a partnership with IIIT-Bangalore to launch PG Diploma programme in machine learning and artificial intelligence. The 11-month Post Graduate Diploma programme in machine learning and artificial intelligence (AI) is a rigorous and selective PG Diploma Programme which will enable learners in mastering concepts in Machine Learning and AI like classification algorithms, deep learning, natural language processing (NLP), reinforcement learning and graph models amongst others. "Colleges and Universities have in-depth knowledge of technical domains and the latest research happening in these domains. IIIT Bangalore brings a strong understanding of evolving areas like machine learning and AI. Hence such a collaboration will help us bring to the learners, the most recent developments in the field." The curriculum is developed by the IIIT-B faculty and leading industry professionals in Indian technology sector.