Home compostable standards
The Australian AS 5810 is a standard that guarantees composting at low temperatures.
Heavy metals and plant toxicity requirements are similar to those for industrial compostability (AS 4736). Biodegradation and disintegration however need to be performed at ambient temperature instead of at elevated temperature (source)
The AS 5810 standard has it's own logo
UNI 11183:2006 is an Italian standard that defines:
the requirements of the plastic materials used to make products that can be disposed by aerobic biodegradation at room temperature . The term "room temperature identify the range of temperature of temperate regions excluding the high temperatures these ones typical for composting. The requirements of ecotoxicity of the plastic materials are also considered in the standard.
The UNI 11183:2006 doesn't seem to be used much (outside of Italy?) and doesn't seem to have a logo.
Besides official government standards, there are 3 logo's that guarantee that you can compost a plastic in your home compost pile and these are:
Note that the Vincotte logo must have the word 'HOME' on the left. Without it, the logo only guarantees that it is compostable in an industrial facility.
Vincotte lists plastic types that are certified home compostable in this PDF
There are several standards that are often mentioned on compostable plastics that guarantee that the plastic can be composted safely (with low levels of heavy metals and toxic substances in the resulting compost). These can theoretically be used in home composting but only when doing hot-composting for a longer period of time, so this won't work on the average home compost heap. Less strict standard first:
The US ASTM D6400
degradation by biological processes during composting to yield CO2, water, inorganic compounds and biomass at a rate consistent with other compostable materials and leaves no visible, distinguishable or toxic residue.... 60% biodegradation within 180 days
The European EN 13432 / Seedling logo
A biodegradation level of at least 90% must be reached in less than 6 months... fragmentation and loss of visibility in the final compost (absence of visible pollution)... absence of negative effects on the composting process... Low levels of heavy metals (below given max values) and absence of negative effects on the final compost.
The Australian AS 4736
Minimum of 90% of plastic materials should disintegrate into less than 2mm pieces in compost within 12 weeks. No toxic effect of the resulting compost on plants and earthworms. Hazardous substances such as heavy metals should not be present above the maximum allowed levels
Again, these 3 standards do not guarantee under which circumstances (temperature) the plastic will compost.