23 research outputs found
Isoelastic Agents and Wealth Updates in Machine Learning Markets
Recently, prediction markets have shown considerable promise for developing
flexible mechanisms for machine learning. In this paper, agents with isoelastic
utilities are considered. It is shown that the costs associated with
homogeneous markets of agents with isoelastic utilities produce equilibrium
prices corresponding to alpha-mixtures, with a particular form of mixing
component relating to each agent's wealth. We also demonstrate that wealth
accumulation for logarithmic and other isoelastic agents (through payoffs on
prediction of training targets) can implement both Bayesian model updates and
mixture weight updates by imposing different market payoff structures. An
iterative algorithm is given for market equilibrium computation. We demonstrate
that inhomogeneous markets of agents with isoelastic utilities outperform state
of the art aggregate classifiers such as random forests, as well as single
classifiers (neural networks, decision trees) on a number of machine learning
benchmarks, and show that isoelastic combination methods are generally better
than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Integrating local information for inference and optimization in machine learning
In practice, machine learners often care about two key issues: one is how to obtain a
more accurate answer with limited data, and the other is how to handle large-scale data
(often referred to as âBig Dataâ in industry) for efficient inference and optimization.
One solution to the first issue might be aggregating learned predictions from diverse
local models. For the second issue, integrating the information from subsets of the
large-scale data is a proven way of achieving computation reduction. In this thesis,
we have developed some novel frameworks and schemes to handle several scenarios
in each of the two salient issues.
For aggregating diverse models â in particular, aggregating probabilistic predictions
from different models â we introduce a spectrum of compositional methods,
RĂ©nyi divergence aggregators, which are maximum entropy distributions subject to
biases from individual models, with the RĂ©nyi divergence parameter dependent on the
bias. Experiments are implemented on various simulated and real-world datasets to
verify the findings. We also show the theoretical connections between RĂ©nyi divergence
aggregators and machine learning markets with isoelastic utilities.
The second issue involves inference and optimization with large-scale data. We
consider two important scenarios: one is optimizing large-scale Convex-Concave Saddle
Point problem with a Separable structure, referred as Sep-CCSP; and the other is large-scale
Bayesian posterior sampling.
Two different settings of Sep-CCSP problem are considered, Sep-CCSP with strongly
convex functions and non-strongly convex functions. We develop efficient stochastic
coordinate descent methods for both of the two cases, which allow fast parallel processing
for large-scale data. Both theoretically and empirically, it is demonstrated that
the developed methods perform comparably, or more often, better than state-of-the-art
methods.
To handle the scalability issue in Bayesian posterior sampling, the stochastic approximation
technique is employed, i.e., only touching a small mini batch of data items
to approximate the full likelihood or its gradient. In order to deal with subsampling error
introduced by stochastic approximation, we propose a covariance-controlled adaptive
Langevin thermostat that can effectively dissipate parameter-dependent noise while
maintaining a desired target distribution. This method achieves a substantial speedup
over popular alternative schemes for large-scale machine learning applications
Smooth markets: A basic mechanism for organizing gradient-based learners
With the success of modern machine learning, it is becoming increasingly
important to understand and control how learning algorithms interact.
Unfortunately, negative results from game theory show there is little hope of
understanding or controlling general n-player games. We therefore introduce
smooth markets (SM-games), a class of n-player games with pairwise zero sum
interactions. SM-games codify a common design pattern in machine learning that
includes (some) GANs, adversarial training, and other recent algorithms. We
show that SM-games are amenable to analysis and optimization using first-order
methods.Comment: 18 pages, 3 figure
Convergence Analysis of Prediction Markets via Randomized Subspace Descent
Abstract Prediction markets are economic mechanisms for aggregating information about future events through sequential interactions with traders. The pricing mechanisms in these markets are known to be related to optimization algorithms in machine learning and through these connections we have some understanding of how equilibrium market prices relate to the beliefs of the traders in a market. However, little is known about rates and guarantees for the convergence of these sequential mechanisms, and two recent papers cite this as an important open question. In this paper we show how some previously studied prediction market trading models can be understood as a natural generalization of randomized coordinate descent which we call randomized subspace descent (RSD). We establish convergence rates for RSD and leverage them to prove rates for the two prediction market models above, answering the open questions. Our results extend beyond standard centralized markets to arbitrary trade networks
ABIDES-Economist: Agent-Based Simulation of Economic Systems with Learning Agents
We introduce a multi-agent simulator for economic systems comprised of
heterogeneous Households, heterogeneous Firms, Central Bank and Government
agents, that could be subjected to exogenous, stochastic shocks. The
interaction between agents defines the production and consumption of goods in
the economy alongside the flow of money. Each agent can be designed to act
according to fixed, rule-based strategies or learn their strategies using
interactions with others in the simulator. We ground our simulator by choosing
agent heterogeneity parameters based on economic literature, while designing
their action spaces in accordance with real data in the United States. Our
simulator facilitates the use of reinforcement learning strategies for the
agents via an OpenAI Gym style environment definition for the economic system.
We demonstrate the utility of our simulator by simulating and analyzing two
hypothetical (yet interesting) economic scenarios. The first scenario
investigates the impact of heterogeneous household skills on their learned
preferences to work at different firms. The second scenario examines the impact
of a positive production shock to one of two firms on its pricing strategy in
comparison to the second firm. We aspire that our platform sets a stage for
subsequent research at the intersection of artificial intelligence and
economics
Multi-period Trading Prediction Markets with Connections to Machine Learning
We present a new model for prediction markets, in which we use risk measures
to model agents and introduce a market maker to describe the trading process.
This specific choice on modelling tools brings us mathematical convenience. The
analysis shows that the whole market effectively approaches a global objective,
despite that the market is designed such that each agent only cares about its
own goal. Additionally, the market dynamics provides a sensible algorithm for
optimising the global objective. An intimate connection between machine
learning and our markets is thus established, such that we could 1) analyse a
market by applying machine learning methods to the global objective, and 2)
solve machine learning problems by setting up and running certain markets
Prediction Markets for Machine Learning: Equilibrium Behaviour through Sequential Markets
Prediction markets which trade on contracts representing unknown future outcomes
are designed specifically to aggregate expert predictions via the market price. While
there are some existing machine learning interpretations for the market price and
connections to Bayesian updating under the equilibrium analysis of such markets,
there is less of an understanding of what the instantaneous price in sequentially
traded markets means. In this thesis I show that the prices generated in sequentially
traded prediction markets are stochastic approximations to the price given by
an equilibrium analysis. This is done by showing that the equilibrium price is a
solution to a stochastic optimisation problem which is solved by stochastic mirror
descent (SMD) by a class of sequential pricing mechanisms. This connection leads to
proposing a scheme called âmini-tradingâ which introduces a parameter related to
the learning rate in SMD. I prove several properties of this scheme and show that it
can improve the stability of prices in sequentially traded prediction markets.
Also I analyse two popular trading models (namely the Maximum Expected Utility
model and the Risk-measure model) in respect to an assumption on the class of
traders I required to interpret sequential markets as SMD. I derive a sufficient condition
for when the Maximum Expected Utility traders satisfy this assumption, but
show that risk-measure based traders naturally satisfy this assumption for the type
of markets I consider. Then I show that the âregretâ of mini-trading markets (with
respect to equilibrium markets) depend on the mini-trade parameter.
Finally I attempt to compare the wealth updates of traders in sequential markets
to the wealth updates in equilibrium markets, since this would help to extend the
interpretation of equilibrium markets as performing Bayesian updates to sequential
markets. For this I present preliminary results
On the Aggregation of Subjective Inputs from Multiple Sources
When we have a population of individuals or artificially intelligent agents possessing diverse subjective inputs (e.g. predictions, opinions, etc.) about a common topic, how should we collect and combine them into a single judgment or estimate? This has long been a fundamental question across disciplines that concern themselves with forecasting and decision-making, and has attracted the attention of computer scientists particularly on account of the proliferation of online platforms for electronic commerce and the harnessing of collective intelligence. In this dissertation, I study this problem through the lens of computational social science in three main parts: (1) Incentives in information aggregation: In this segment, I analyze mechanisms for the elicitation and combination of private information from strategic participants, particularly crowdsourced forecasting tools called prediction markets. I show that (a) when a prediction market implemented with a widely used family of algorithms called market scoring rules (MSRs) interacts with myopic risk-averse traders, the price process behaves like an opinion pool, a classical family of belief combination rules, and (b) in an MSR-based game-theoretic model of prediction markets where participants can influence the predicted outcome but some of them have a non-zero probability of being non-strategic, the equilibrium is one of two types, depending on this probability -- either collusive and uninformative or partially revealing; (2) Aggregation with non-strategic agents: In this part, I am agnostic to incentive issues, and focus on algorithms that uncover the ground truth from a sequence of noisy versions. In particular, I present the design and analysis of an approximately Bayesian algorithm for learning a real-valued target given access only to censored Gaussian signals, that performs asymptotically almost as well as if we had uncensored signals; (3) Market
making in practice: This component, although tied to the two previous themes, deals more directly with practical aspects of aggregation mechanisms. Here, I develop an adaptation of an MSR to a nancial market setting called a continuous double auction, and document its
experimental evaluation in a simulated market ecosystem