Private Learning Implies Online Learning: An Efficient Reduction

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online learning from expert advice

Boosting Simple Learners

Boosting is a celebrated machine learning approach which is based on the idea of combining weak and moderately inaccurate hypotheses to a strong and accurate one. We study boosting under the assumption that the weak hypotheses belong to a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are "rules-of-thumbs" from an "easy-to-learn class". (Schapire and Freund '12, Shalev-Shwartz and Ben-David '14.) Formally, we assume the class of weak hypotheses has a bounded VC dimension. We focus on two main questions: (i) Oracle Complexity: How many weak hypotheses are needed in order to produce an accurate hypothesis? We design a novel boosting algorithm and demonstrate that it circumvents a classical lower bound by Freund and Schapire ('95, '12). Whereas the lower bound shows that $\Omega({1}/{\gamma^2})$ weak hypotheses with $\gamma$-margin are sometimes necessary, our new method requires only $\tilde{O}({1}/{\gamma})$ weak hypothesis, provided that they belong to a class of bounded VC dimension. Unlike previous boosting algorithms which aggregate the weak hypotheses by majority votes, the new boosting algorithm uses more complex ("deeper") aggregation rules. We complement this result by showing that complex aggregation rules are in fact necessary to circumvent the aforementioned lower bound. (ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class? Can complex concepts that are "far away" from the class be learned? Towards answering the first question we identify a combinatorial-geometric parameter which captures the expressivity of base-classes in boosting. As a corollary we provide an affirmative answer to the second question for many well-studied classes, including half-spaces and decision stumps. Along the way, we establish and exploit connections with Discrepancy Theory.Comment: A minor revision according to STOC review

Dual-Input Switched Capacitor Converter Suitable for Wide Voltage gain Range

International audienceThe capacitive-based switching converter suffers from low efficiency, except for a few conversion ratios, thus limiting its use in fine dynamic voltage and frequency scaling for the power management of digital circuits. Therefore, this paper proposes a Multiple Input Single Output Switched Capacitor Converter (MISO-CSC) to provide flatness efficiency over a large voltage gain range. First, the power efficiency calculation in MISO configuration is given, and then the best ones to optimize the number of switched capacitor structures is selected. By using two power supplies, the MISO converter produces 18 ratios instead of three in SISO (Single Input Single Output) mode. Using a CMOS 65nm technology, the transistor-based simulations exhibit an average 15% efficiency gain over a 0.5-1.4V output voltage range compared to the SISO-CSC. Index Terms— switched capacitor converter, multi-input converter, power efficiency optimization, fully integrated voltage regulator, dynamic voltage and frequency scaling

Galois groups over rational function fields over skew fields

Let $H$ be a skew field of finite dimension over its center $k$. We solve the Inverse Galois Problem over the field of fractions $H(X)$ of the ring of polynomial functions over $H$ in the variable $X$, if $k$ contains an ample field

Elucidating the effect of tomato leaf surface microstructure on Botrytis cinerea using synthetic systems

For some pathogenic fungi, sensing surface topography is part of their infection strategy. Their directional growth and transformation to a new developmental stage is influenced by contact with topographic features, which is referred to as thigmo-response, the exact functionality of which is not fully understood. Research on thigmo-responses is often performed on biomimetically patterned surfaces (BPS). Polydimethylsiloxane (PDMS) is especially suitable for fabrication of BPS. Here, we used synthetic BPS surfaces, mimicking tomato leaf surface, made from PDMS with the pathogenic fungus Botrytis cinerea to study the influence of structural features of the leaf surface on the fungus behavior. As a control, a PDMS surface without microstructure was fabricated to maintain the same chemical properties. Pre-penetration processes of B. cinerea, including the distribution of conidia on the surface, germination, and germ tube growth were observed on both leaf-patterned and flat PDMS. Microstructure affected the location of immediate attachment of conidia. Additionally, the microstructure of the plant host stimulated the development of germ tube in B. cinerea, at a higher rate than that observed on flat surface, suggesting that microstructure plays a role in fungus attachment and development.Peer Reviewe